A  PRACTICAL  APPLICATION  OF  PHYSICS 


HOUSEHOLD     PHYSICS 


BY 
C.    H.    BRECHNER 

FORMERLY   TEACHER    OF    PHYSICS    IN    THE 

EAST   TECHNICAL   HIGH    SCHOOL 

CLEVELAND 


ALLYN    AND    BACON 

BOSTON  NEW   YORK  CHICAGO 

ATLANTA  S^  N    FRANCISCO 


_ 

COPYRIGHT,  1919 
BY  C.    H.    BRECHNER 


J.  8.  Gushing  Co.  —  Berwick  &  Smith  Co, 
Norwood,  Mass.,  U.S.A. 


PREFACE 

Household  Physics  was  written  primarily  for  girls.  The 
principles  of  physics  in  such  a  book  are  of  course  the  same 
as  in  a  text-book  for  boys  or  for  mixed  classes.  But  in 
Household  Physics  these  principles  are  applied  in  such  a 
way  as  to  interest  girls,  by  using  examples  and  references 
with  which  they  are  thoroughly  familiar. 

The  work  was  developed  in  the  classroom.  At  first  the 
author  used  an  outline,  filling  in  with  applications  and 
drawings  in  the  recitation  periods.  The  following  year  the 
text  was  written  and  mimeograph  copies  put  into  the  hands 
of  the  students.  After  this  material  had  been  carefully 
worked  over  with  various  classes,  it  was  revised  into  the 
present  book. 

The  subject  of  Heat  is  taken  up  first,  since  it  is  one  which 
has  many  applications  of  vital  importance  to  the  household. 
Thus  the  girl  becomes  interested  in  physics  from  the  first, 
and  looks  forward  to  recitations  with  pleasure. 

The  language  of  the  book  has  been  kept  as  simple  as 
possible  throughout.  The  topics  are  carefully  explained 
and  these  explanations  are  illustrated  by  a  wealth  of  line 
drawings  and  photographs.  The  problems  are  especially 
easy  and  practical. 

The  author  wishes  to  take  this  opportunity  to  thank  the 
several  industrial  concerns  which  supplied  many  of  the 
photographs,  and  also  those  teachers  and  pupils  who  so 
kindly  assisted  him  in  bringing  the  work  to  completion. 

C.  H.  B. 

AUGUST,  1919. 

v 


CONTENTS 

CHAPTER  PAGE 

I.     HEAT  AND  HEAT  MEASUREMENT 1 

II.    EXPANSION 29 

III.  HEAT  TRANSFERENCE 41 

IV.  SOURCES  OF  HEAT 60 

V.    WAVE  MOTION 67 

VI.    SOUND 74 

VII.  BASIS  FOR  Music          .        .        .        .       f.        .        .85 

VIII.     LIGHT    .                91 

IX.     REFLECTION  AND  MIRRORS 96 

X.    REFRACTION  AND  LENSES 103 

XI.  ILLUMINATION  AND  CANDLE  POWER     ....  127 

XII.     COLOR 132 

XIII.  MAGNETISM 146 

XIV.  ELECTRICITY. 153 

XV.  MAGNETIC  EFFECT  OF  AN  ELECTRICAL  CURRENT         .  163 

XVI.  HEATING  EFFECT  OF  AN  ELECTRIC  CURRENT       .        .173 

XVII.  MOTION-PRODUCING  EFFECT  OF  AN  ELECTRIC  CURRENT  184 

XVIII.     INDUCTION 200 

XIX.  CHEMICAL  RELATION  OF  AN  ELECTRICAL  CURRENT     .  212 

XX.     BATTERIES 217 

XXI.    MECHANICS  OF  SOLIDS 227 

XXII.    MACHINES 23^ 

XXIII.  DYNAMICS 248 

XXIV.  MECHANICS  OF  FLUIDS 259 

Appendix 285 

Index .        .  297 

vii 


HOUSEHOLD   PHYSICS 

CHAPTER  I 
HEAT  AND   HEAT   MEASUREMENT 

1.   Nature  of  Heat.  —  Physics  is  a  study  of  the  e very-day 
events  of  life.    It  is  defined  as  the  science  of  matter  and  energy. 


TAKING  THE  TEMPERATURE  OF  MELTING  ICE  TO  DETERMINE  THE  MELTING 
OR  FREEZING  POINT. 

Matter  is  anything  which  occupies  space ;   e.g.  air,  water, 
wood,  iron,  etc.     Energy  is  ability  to  do  work. 

1 


2  HF^T  :AND   HEAT   MEASUREMENT 

The  student  of  domestic  science  must  often  wonder  why 
some  of  the  remarkable  things  in  cooking,  freezing,  and  melt- 
ing happen  as  they  do.  One  of  the  divisions  of  physics,  the 
subject  of  heat,  touches  closely  many  of  the  things  done  in 
domestic  science  work ;  and  it  has  a  vital  relation  to  the  coal 
and  gas  bills  at  home. 

Heat  is  one  form  of  energy,  and  is  of  two  kinds,  molecular 
heat  and  radiant  heat;  sometimes  called  sensible  heat  and 
insensible  heat.  Sensible  heat  can  be  detected  by  the  senses, 
while  insensible  heat  cannot. 

All  substances  are  composed  of  molecules,  or  very  small  particles  of 
matter,  which  are  never  at  rest  but  are  always  vibrating  with  great 
rapidity.  In  a  hot  body  they  vibrate  faster  than  in  a  cold  body. 
When  you  heat  a  flat-iron  you  make  the  molecules  jump  faster.  If 
you  rub  your  hands  together,  they  are  warmed  by  the  increased  vibra- 
tion of  the  molecules. 

The  energy  which  molecules  possess,  due  to  their  vibra- 
tion, is  called  sensible  heat  or  molecular  heat.  Put  your 
hand  on  anything  hot  and  you  will  see  how  easily  sensible 
heat  can  be  detected  by  the  sense  of  touch. 

Heat  comes  all  the  way  from  the  sun  to  the  earth.  It 
travels  through  air  or  clear  glass  without  warming  it ;  but 
when  it  strikes  any  object  not  transparent  it  is  absorbed 
and  warms  the  object.  Heat  passing  through  the  air  is 
insensible  or  radiant  heat,  but  when  it  strikes  a  non- 
transparent  object  it  is  changed  to  sensible  or  molecular 
heat. 

If  you  touch  a  window  pane  when  the  sun  is  shining 
through,  the  glass  feels  cold.  If  you  touch  a  piece  of  black 
cloth  lying  in  sunshine,  it  feels  warm. 

Either  form  of  heat  may  be  changed  into  the  other.  Sen- 
sible heat  in  the  glowing  coals  of  the  fireplace  starts  out  as 


TEMPERATURE  3 

radiant  heat,  or  vibration  in  ether ;  but  when  it  strikes  you, 
it  is  changed  back  to  sensible  heat. 

2.  Hot  and  Cold.  —  Hot  and  cold  are  common  words  used 
to  denote  how  a  body  feels  to  the  touch.  They  are  only  rela- 
tive terms,  and  are  not  very  definite.  The  term  cold  is 


TAKING  THE  TEMPERATURE  OF  STEAM  OVER  BOILING  WATER  TO 
DETERMINE  THE  BOILING  POINT. 

negative  in  meaning,  and  refers  to  the  absence  of  heat.  Cold 
does  not  come  into  your  house ;  but  heat  goes  out,  leaving  it 
cold,  or  without  heat. 

3.  Temperature.  —  Since  the  terms  hot  and  cold  do  not 
give  us  a  definite  means  of  expressing  the  heat  condition  of 
bodies,  we  use  another  word,  temperature.  Temperature  is 


4  HEAT   AND   HEAT   MEASUREMENT 

the  measurement  of  the  speed  of  vibration  of  the  molecules  of  an 
object;  that  is,  it  is  a  means  of  expressing  the  hotness  of  a 
body. 

4.  Thermometers.  —  Since  the  sense  of  feeling  is  inac- 
curate, we  must  have  some  definite  means  of  measuring 
temperature ;  and  for  such  purpose  we  use  the  thermometer. 

Most  substances  expand  when  heated,  and  contract 
when  heat  is  removed.  This  expansion  is  used  to  measure 
temperature.  Mercury  expands  or  contracts  rapidly  and 
evenly,  and  therefore  is  commonly  used  as  the  expanding 
substance  in  thermometers.  Sometimes  alcohol  containing 
red  dye  takes  its  place.  There  are  several  kinds  of  ther- 
mometers, and  we  must  be  familiar  with  two,  —  Centi- 
grade and  Fahrenheit. 

The  best  way  to  understand  these  is  to  learn  how  they 
are  made,  and  how  the  scales  are  placed  on  them.  First 
we  must  have  some  fixed  point,  that  is,  some  point  which  will 
mean  the  same  temperature  everywhere  in  the  world.  Pure 
water  furnishes  such  a  point,  as  it  freezes  (changes  from  liquid 
to  solid),  or  melts  (changes  from  solid  to  liquid),  always  at 
the  same  temperature,  under  uniform  atmospheric  condi- 
tions. For  another  fixed  point  the  boiling  temperature  of 
pure  water,  under  uniform  atmospheric  conditions,  is  taken. 

In  making  a  thermometer,  take  a  glass  tube  of  small 
uniform  bore  with  a  bulb  at  one  end.  Fill  it  partly  with 
mercury,  removing  all  air;  then  seal  it.  To  put  on  the 
Centigrade  scale,  place  the  bulb  in  cracked  ice  and  when 
the  mercury  stops  falling  make  a  scratch  on  the  glass  op- 
posite this  point  and  mark  it  "  0°." 

Next  place  the  bulb  in  the  steam  just  above  water  boil- 
ing under  normal  pressure.  When  the  mercury  stops  rising, 
mark  this  point  "  100°."  Divide  the  space  between  into 


CHANGING  FROM   ONE  SCALE   TO   THE   OTHER      5 


100  equal  divisions,  each  one  representing  one  degree  change 
of  temperature.  This  is  the  most  convenient  thermometer 
scale  we  have,  since  one  of  the  fixed  points  is  at  0°.  How- 
ever, since  the  Fahrenheit  scale  is  more  commonly  used  in 
this  country,  we  must  learn 

Jjl  /~1 

that  also   and  how  to  change 

from  one  to  the  other.  212  -hi  100 

On  the  Fahrenheit  scale  the 

freezing  temperature  of   water     180  Degrees  \        100  Degrees 
is  marked  "  32°,"  and  the  boil-     . 
ing  point  "212°."     The  space  32 

between   is   then   divided   into 
180  equal  parts,  each  called  a    FlGURE    !•  —  FIXED    POINTS   ON 

j  THE  CENTIGRADE  AND   FAHREN- 

aegree.  HEIT  ScALES> 

5.  Relation     of     the     Two 

Scales.  —  The  relation  between  the  two  scales  is  shown  in 
Figure  1.  A  little  study  of  this  figure  will  show  you  that 
an  equal  space  is  divided  into  100  Centigrade  degrees  and 
180  Fahrenheit  degrees.  This  means  that  the  C.  degree  is 
almost  twice  as  large  as  the  F.  degree. 


F 

C 

212 

100 

68  F 

?-20°C 

36° 

?-ao 

32 

0 

F                C 

That  is,  100°  C.  =  180°  F.,  or 

1°C.  -WF.,or*0F.;and 

212 

100 

180°  F.  =  100°  C.,  or 

1°  F.  =  iSS0  F.,  or  |°  F. 

>8°F 

|  20°  C 

6.   Changing       from 

=36  < 

20° 

One  Scale  to  the  Other. 

32 

0 

-To  change  from  one 

scale  to  the   other  al- 

r 

ways  make  a  sketch  as 

FIGURE  2.  -SHOWING  HOW  TO  CHANGE  FROM    shown  in  FiSure  2>  and 
ONE  SCALE  TO  THE  OTHER.  solve  as  follows  : 


6  HEAT   AND   HEAT   MEASUREMENT 

Problem  :  Change  68°  F.  to  the  corresponding  Centigrade  reading. 
68°  F.  -  32°  F.  =  36°  F.  above  the  fixed  freezing  point,  (a)  Figure  2. 
36  X  i  =  20°  C.  above  the  freezing  point  on  the  Centigrade  scale. 
Therefore  20°  C.  is  the  corresponding  Centigrade  reading. 

Problem :   Change  20°  C.  to  F.  reading. 

20°  C.  is  20°  above  freezing  point. 

20  X  £  =  36°  F.  above  freezing  point  on  F.  scale,  (6)  Figure  2. 

But  freezing  on  F.  scale  is  32°  F. 

Therefore  32°  F.  +  36°  F.  =  68°  F.,  Fahrenheit  reading. 

Problems 

1.  Change  from  Centigrade  to  Fahrenheit  readings :   40°  C.,  —  10° 
C.,  -  40°  C. 

2.  Change  from  Fahrenheit  to  Centigrade  readings  :  60°  F.,  22°  F., 
40°  F. 

3.  A  change  of  temperature  of  28°  C.  equals  what  change  of  tem- 
perature on  the  Fahrenheit  scale? 

4.  A  range  of  48°  F.  equals  what  range  on  the  Centigrade  scale  ? 

7.  Freezing  and  Boiling  Points.  —  We  have  already  said 
that  the  freezing  point  is  the  temperature  at  which  a  liquid 
changes  to  a  solid.  Such  substances  as  iron,  lead,  gold, 
paraffine,  and  mercury  have  a  freezing  or  melting  point, 
each  differing  from  the  others.  As  you  have  already  learned, 
in  making  ices  and  ice  cream,  putting  salt  on  the  ice  lowers 
its  melting  temperature ;  that  is,  a  salt  solution  has  a  lower 
freezing  point  than  pure  water. 

When  you  put  a  kettle  of  water  on  the  stove  to  boil,  how 
do  you  know  when  it  is  boiling?  It  is  not  when  the  vapor 
begins  to  come  from  the  kettle,  but  when  it  bubbles  freely. 

If  a  thermometer  is  placed  in  a  pan  of  cold  water  over  a 
flame,  the  mercury  gradually  rises.  When  bubbles  begin 
to  come  out  of  the  water,  the  mercury  becomes  stationary 
and  will  never  rise  higher,  no  matter  how  long  or  how  rapidly 


FREEZING  AND  BOILING  POINTS  7 

you  heat  the  water,  if  the  bubbles  are  free  to  escape.  If 
you  examine  the  escaping  bubbles  at  such  a  time,  you  will 
find  that  they  form  at  the  bottom  of  the  vessel,  where  the 
heat  is  applied,  rise  to  the  top,  and  break.  They  are  not 
bubbles  of  air,  but  are  bubbles  of  steam,  able  to  push  the 
air  and  water  back  and  thus  get  out  of  the  water.  These 
steam  bubbles  have  the  same  kind  of  molecules  as  liquid 
water,  but  the  molecules  are  so  far  apart  that  they  form  a 
gas  instead  of  a  liquid. 

The  boiling  point  is  that  temperature  at  which  the  vapor 
tension  is  equal  to  the  applied  pressure.  The  vapor  tension 
is  the  pressure  exerted  by  the  molecules  of  the  vapor  trying 
to  escape.  The  applied  pressure  is  the  pressure  of  the  sur- 
rounding element. 


Freezing  and  Boiling  Points  of  Some  Common  Substances 
Under  Normal  Atmospheric  Pressure 


SUBSTANCE 

FREEZING  PT. 

BOILING    PT. 

Oxvffcn 

Centigrade 

-  235° 

Centigrade 

-  182° 

Ammonia       

-    75° 

-    39° 

Ether   .     .                        .... 

-  113° 

35° 

Methylic  Alcohol 

-  112° 

66° 

Distilled  Water       ....... 

0° 

100° 

Acetic  Acid   

17° 

117° 

Turpentine 

-    27° 

157° 

Fat,  Oil  etc. 

-    33° 

210° 

Mercury   

-    38.8° 

357° 

Hardly  any  two  substances  have  the  same  freezing  or 
boiling  points  and  some  are  used  for  specific  purposes  be- 
cause of  this.  Mercury,  for  example,  is  used  in  the  ther- 


8  HEAT   AND-  HEAT   MEASUREMENT 

mometer  because  its  freezing  point  is  low  and  its  boiling 
point  is  high.  Ammonia  is  used  in  the  manufacture  of 
artificial  ice  because  its  boiling  point  is  low.  Doughnuts 
are  dropped  into  hot  fat  instead  of  water  because  fat 
boils  at  about  400°  F.  and  so  can  be  made  hotter  than 
water. 

8.  Effect  of  Pressure  on  Freezing  and  Boiling  Points.  — 
When  water  is  placed  under  a  pressure  it  becomes  more 
difficult  to  freeze;  that  is,  its  freezing  point  is  lowered. 
Under  normal  atmospheric  pressure  water  freezes  at  0°  C. 
or  32°  F.,  but  if  it  is  put  under  a  higher  pressure  it  must 
be  cooled  to  a  temperature  lower  than  0°  C.  or  32°  F.  before 
it  will  freeze. 

An  example  of  this  is  to  be  had  in  pressing  a  snow-ball. 
A  good  time  for  snow-balling  is  when  the  snow  is  damp, 
that  is,  when  it  is  at  the  freezing  point.  The  loose  snow 
is  taken  in  the  hands  and  pressed.  This  increased  pressure 
lowers  the  freezing  point  below  the  temperature  of  the 
snow,  and  part  of  it  melts.  Then  when  the  pressure  is 
removed  the  freezing  point  again  goes  up  to  0°  C.,  and  the 
melted  snow  freezes  again,  making  the  ball  hard. 

If  water  were  put  into  a  strong  vessel  and  sufficient 
pressure  were  applied,  the  water  would  stay  a  liquid,  even 
in  our  coldest  weather. 

The  effect  of  pressure  on  the  boiling  point  is  just  the 
opposite  of  what  it  is  on  the  freezing  point ;  that  is,  pressure 
raises  the  boiling  point.  Instead  of  boiling  at  100°  C.  or 
212°  F.,  the  water  must  be  made  hotter  when  a  pressure 
above  that  of  the  normal  atmosphere  is  put  on  it.  Water 
in  the  boiler  of  a  locomotive  under  a  pressure  of  200  pounds 
per  square  inch  boils  at  380°  F.  instead  of  at  212°  F.  On 
the  other  hand,  water  under  a  pressure  less  than  normal 


EFFECT  OF  PRESSURE   ON   THE  BOILING  POINT     9 


FIGURE  3.  —  A 
PRESSURE  KETTLE. 


atmospheric   pressure    boils   at   a   lower   temperature   than 
212°  F.    / 

9.  Application  of  Effect  of  Pressure  on  the  Boiling  Point. 
-  Water  in  an  open  kettle  boils  at  a  comparatively  low  tem- 
perature on  the  top  of  a  high  mountain 
because  the  pressure  of  the  air  is  much 
less  than  at  the  sea  level.  Sometimes 
this  temperature  is  lower  than  the  cook- 
ing temperature  of  starch ;  and  so  at  high 
elevations  it  is  possible  to  put  potatoes 
into  an  open  kettle  and  boil  the  water 
freely,  without  cooking  the  potatoes.  In 
the  mountains  this  difficulty  is  sometimes 
overcome  by  using  a  pressure  kettle  (Figure  3),  that  is, 
a  kettle  with  a  lid  screwed  on,  making  it  air-tight.  This 
lid  holds  the  steam  in  the  kettle  and  increases  the  pressure, 
thereby  raising  the  boiling  point  above  the  cooking  tem- 
perature. 

Gelatin   is   a   product   which   comes  from  the    bones  of 
animals.     To    extract    it    from    the    bones    a    temperature 

higher  than  100°  C.  is  necessary. 
To  get  this  higher  temperature 
the  bones  are  cooked  in  a  closed 
vessel,  under  pressure.  (Figure  3.) 
In  the  manufacture  of  sugar  the 
principal  thing  is  to  evaporate  the 
water  from  the  juice  of  the  sugar 
cane  or  sugar  beet.  This  is  done 
by  boiling,  but  when  the  syrup 
begins  to  get  thick,  it  is  easily 
burned;  so  it  is  put  into  vacuum  pans  (Figure  4)  which 
are  closed,  and  part  of  the  air  and  steam  is  pumped  out, 


Suction 


FIGURE  4.  —  A  VACUUM  PAN. 


10  HEAT   AND   HEAT    MEASUREMENT 

making  the  pressure  inside  lower  than  that  of  the  atmos- 
phere. This  causes  the  syrup  to  boil  at  a  lower  temperature, 
and  so  prevents  scorching  of  the  sugar. 

10.  Quantity  of  Heat.  —  Temperature  and  quantity  of  heat 
mean  very  different  things.     The  water  in  a  tea-kettle  may 
be  at  the  same  temperature  as  the  water  in  a  lake ;   yet  the 
lake  would  have  much  more  heat.     Even  if  the  water  in 
the  tea-kettle  were  boiling,  the  lake  would  have  more  heat, 
though  the  water  in  it  might  be  ice-cold. 

The  term  quantity  of  heat  does  not  refer  to  the  tempera- 
ture of  the  body,  but  denotes  the  amount  of  energy  in  the 
vibration  of  its  molecules. 

11.  Heat  Units.  —  The  quantity  of  heat  can  be  measured, 
but  not  by  our  familiar  units  of  pound,  gallon,  foot,    etc. 
Other  kinds  of  units  must  be  used,  and  these  are  based 
on  the  effect  produced  upon  water  when  heat  is  applied. 
They  are  B.  T.  U.  (British  Thermal  Unit),  calory,  and  great 
calory. 

The  B.  T.  U.  is  the  amount  of  heat  required  to  raise 
the  temperature  of  1  pound  of  water  1°  F.  The  calory  is 
the  amount  of  heat  required  to  raise  the  temperature  of  1 
gram  of  water  1°  C.  The  great  calory  is  1000  calories. 

In  these  definitions  we  see  that  no  certain  degree  is  men- 
tioned. This  is  because  it  takes  approximately  the  same 
amount  of  heat  to  raise  the  temperature  of  a  certain  amount 
of  water  any  one  degree  as  to  raise  it  any  other  degree. 

Although  the  calory  and  B.  T.  U.  are  units  of  two  distinct 
systems,  there  is  a  definite  relation  between  them.  For 
all  practical  purposes,  1  B.  T.  U.  equals  250  calories,  or  1 
great  calory  equals  4  B.  T.  U.'s. 

12.  Heat  of  Fusion.  —  If  a  piece  of  ice  is  placed  in  a  pan 
on  the  stove,  the  ice  begins  to  melt;    but  the  temperature 


HEAT  OF  FUSION  11 

of  the  water  does  not  rise.  Both  the  ice  and  the  water 
stay  at  0°  C.  or  32°  F.  until  all  the  ice  is  melted.  After 
that,  the  water  begins  to  get  warmer.  The  question  is : 
Where  did  all  the  heat  go  while  the  ice  was  melting?  It 
was  used  to  melt  the  ice. 

As  we  have  learned,  everything  that  occupies  space  is 
made  up  of  small  particles,  called  molecules.  When  the 
water  is  frozen  solid,  these  molecules  are  drawn  together 
by  a  force  called  cohesion  ;  and  this  force  keeps  them  in 
place.  When  the  ice  melts,  the  molecules  are  torn  apart, 
and  slip  past  one  another,  making  it  possible  to  pour  the 
water.  To  tear  these  molecules  apart  requires  energy; 
and  this  energy  is  the  heat  which  melts  the  ice. 

In  other  words,  we  can  say:  While  the  ice  is  melting, 
the  heat  supplied  is  used  to  tear  the  molecules  apart,  chang- 
ing the  solid  to  a  liquid. 

Some  substances  require  more  energy  to  tear  the  mole- 
cules apart  than  others ;  so  in  order  to  melt  some  substances 
more  heat  is  required  than  to  melt  others.  The  heat  required 
to  change  a  unit  mass  of  a  substance  from  a  solid  to  a  liquid 
is  called  the  heat  of  fusion  of  that  substance. 

If  a  pound  of  ice  at  32°  F.  were  put  on  the  stove  and 
heated,  it  would  have  to  take  up  144  B.  T.  U.'s  before  it 
would  be  all  melted.  If  a  gram  of  ice  were  used  instead  of 
a  pound,  80  calories  would  be  required  to  melt  it. 

The  heat  of  fusion  of  ice  is  the  amount  of  heat  required  to 
melt  1  pound  of  ice  without  changing  its  temperature.  This 
has  been  found  to  be  144  B.  T.  U.'s.  (English  system.) 

Or,  the  heat  of  fusion  of  ice  is  the  amount  of  heat  required 
to  melt  1  gram  of  ice  without  changing  its  temperature.  This 
has  been  found  to  be  80  calories.  (Metric  system.) 

On  the  other  hand,  when  water  freezes,  it  gives  out  as 


12 


HEAT   AND   HEAT   MEASUREMENT 


much  heat  as  it  takes  in  when  the  same  weight  of  ice  melts ; 

that  is,  when  1   pound  of  water  freezes,  it  gives  off  144 

B.  T.  U.'s;    and  when  1  gram  of  water  freezes,  it  gives  off 

80  calories. 

13.   The  Refrigerator.  —  Every  one  is  familiar  with  the 

refrigerator.     It  is  a  box  with  special  walls  so  constructed 

that  heat  cannot 
easily  get  through 
them.  A  com- 
partment is  made 
to  put  ice  in,  and 
at  least  one  other 
compartment  is 
made  to  hold  the 
butter,  meat,  fruit 
or  any  article  one 
wishes  to  keep 
cold.  Later  a 
more  thorough 
study  will  be  made 
of  the  construc- 
tion of  the  refrig- 
erator. All  we 
are  interested  in 
now  is  that  it  is 
a  box  in  which  to 

place  ice  to  keep  articles  cool  so  they  will  remain  fresh. 
The  ice,  when  placed  in  the  refrigerator,  begins  to  melt; 

but,  to  melt,  it  must  have  heat.     It  takes  the  heat  from 

the  other  things  in  the  refrigerator;    and  thus  keeps  them 

cool.     For  every  pound  of  ice  that  melts,  144  B.  T.  U.'s 

must  be  used  up. 


FIGURE  5. — A  REFRIGERATOR. 


FREEZING  ICE  CREAM 


13 


FIGURE  6.  —  LINE  DRAWING  OF  AN 
ICE  CREAM  FREEZER. 


Two  refrigerators  can  be  tested  as  follows :    Place  equal 

weights  of  ice  in  the  two  empty  refrigerators.     Close  the 

doors,  and  note  the  time  re- 
quired for  the  ice  to  melt  in 

each.     The  one  in  which  the 

ice  melts  first  lets  in  the  more 

heat,    and    hence    is    not    so 

good  as  the  one  in  which  the 

ice  lasts  longer. 

14.   Freezing  Ice  Cream.  — 

The  freezer  in  which  ice  cream 

and  ices  are  frozen  is  made  up 

of  two  compartments ;  one,  a 

can,   which    fits   very   loosely 

into  the  other,  a  wooden  pail. 

(Figure  6.) 
The  cream,  with  its  other  ingredients,  is  placed  in  the 

inner  can,  which,  in  turn,  is  placed  in  the  wooden  pail. 

Cracked  ice,  mixed  with  salt,  is  packed  firmly  around  the 

can.  Then  the  can  is 
kept  turning,  so  that 
the  cream  will  not  freeze 
in  lumps.  But  what 
makes  the  cream  freeze 
at  all?  When  the  ice 
begins  to  melt  it  takes 
the  heat  from  the  cream, 
thus  reducing  its  tem- 
perature. 

But  the  cream  would 
never  freeze  if  salt  had 
not  been  put  on  the  ice. 


FIGURE  7.  —  PHOTOGRAPH  OF  AN  ICE 
CREAM  FREEZER. 


14  HEAT   AND   HEAT   MEASUREMENT 

When  pure  ice  melts,  its  temperature  is  0°  C.  or  32°  F.,  a 
temperature  at  which  cream  will  not  freeze.  But  when 
salt  is  mixed  with  the  ice,  the  freezing  point  is  lowered 
until  the  temperature  has  been  reduced  several  degrees 
below  0°  C.  or  32°  F.  This  low  temperature  causes  the 
cream  to  freeze. 

Salt  is  also  used  to  melt  the  ice  on  a  sidewalk  in  the  winter 
time.  The  salt  reduces  the  freezing  point  of  the  ice  to  a 
point  below  the  temperature  of  the  air,  and  so  it  melts, 
even  though  the  water  is  still  freezing  in  the  gutter. 

15.  Getting    Heat   from    Freezing   Water.  —  Sometimes 
when  the  weather  is  likely  to  be  cold  enough  to  freeze  the 
vegetables  and  fruits  in  the  cellar,   farmers  put  tubs  of 
water  in  the  cellar  to  protect  them.     If  water  is  in  the 
cellar,  it  will  begin  to  freeze  just  as  soon  as  the  temperature 
gets  as  low  as  0°  C.  or  32°  F.     The  vegetables  and  fruits 
will  not  freeze  at  this  temperature,  because  they  contain 
solutions  of  sugar.     As  the  heat  leaks  out  of  the  cellar, 
more  water  freezes,  giving  up  its  144  B.  T.  U.'s  per  pound, 
and  keeping  the  temperature  up  to  0°  C.  or  32°  F. 

This  goes  on  as  long  as  there  is  any  water  left  unfrozen; 
and  so  protects  the  vegetables  and  fruits.  Should  all  the 
water  freeze,  then  the  temperature  may  fall  low  enough  for 
these  things  to  freeze  also ;  therefore,  large  tubs  are  used. 

16.  Effect  of  Heat  of  Fusion  on  Climate.  —  In  regions 
near  large  bodies  of  water  the  climate  is  affected  by  the 
high  heat  of  fusion  of  water.     The  general  effect  is  to  make 
both  fall  and  spring  come  later. 

At  the  end  of  summer,  as  the  weather  gets  colder  and 
colder,  the  water  begins  to  freeze.  As  it  freezes,  it  gives  off 
144  B.  T.  U.'s  per  pound,  and  thus  keeps  the  temperature 
up  to  0°  C.  or  32°  F. ;  just  as  putting  water  in  the  cellar 


HEAT  OF   VAPORIZATION  15 

to  keep  the  vegetables  from  freezing  kept  the  temperature 
of  the  cellar  up  to  0°  C.  or  32°  F.  This,  then,  causes  the 
fall  to  be  late. 

Again,  at  the  end  of  winter,  when  the  weather  gets  warmer, 
the  ice  begins  to  melt.  In  melting,  it  takes  in  144  B.  T.  U.'s 
for  every  pound;  and  so  keeps  the  temperature  down  to 
0°  C.  or  32°  F. ;  just  as  putting  ice  in  the  refrigerator  keeps 
the  things  in  it  cold.  Thus,  the  spring  is  also  late. 

This  fact  has  much  to  do  with  fruit-raising.  More  fruit 
is  destroyed  by  changeable  weather  in  the  spring  than  by 
anything  else.  If  a  few  warm  days  come  the  last  of  March 
or  the  first  of  April,  the  buds  on  the  fruit  trees  start.  Then, 
if  a  cold  snap  comes,  the  buds  are  frozen,  and  the  fruit  is 
ruined.  Near  a  large  body  of  water  the  melting  ice  may 
prevent  a  warm  period  early  in  the  season,  so  that  the  buds 
do  not  start  until  there  is  no  danger  of  frosts. 

Problems 

1.  How  many  B.  T.  U.'s  are  required  to  melt  50  Ib.  of  ice  in  a  re- 
frigerator ?     Where  does  the  heat  come  from  ? 

2.  When  a  tub  of  water,  weighing  60  Ib.,  is  placed  in  the  cellar, 
and  it  all  freezes,  how  much  heat  is  given  up?     Where  does  the  heat 
go? 

3.  How  many  calories  are  required  to  melt  25  grams  of  ice  at  0°  C. 
and  raise  its  temperature  to  boiling? 

4.  If  100  grams  of  ice  at  0°  C.  are  placed  in  400  grams  of  water  at 
30°  C.,  and  if,  after  all  the  ice  is  melted,  the  temperature  is  8°  C.,  how 
much  heat  was  given  up  by  each  gram  of  ice  in  melting? 

17.  Heat  of  Vaporization.  —  If  a  pan  of  water  is  placed 
on  the  stove  and  heated,  its  temperature  gradually  rises 
until  the  water  begins  to  boil.  After  that,  the  temperature 
remains  constant  until  all  the  water  is  boiled  away,  just 
as  in  the  preceding  experiment  the  temperature  remained 


16  HEAT   AND   HEAT   MEASUREMENT 

constant  until  all  the  ice  was  melted.  While  the  water  is 
boiling,  the  heat  supplied  goes  to  change  the  liquid  to  a  gas. 

We  have  seen  that  it  takes  heat  to  change  ice  to  a  liquid 
and  that  the  heat  is  used  to  tear  the  molecules  apart.  The 
same  thing  happens  when  a  liquid  is  changed  to  a  gas.  In 
the  form  of  a  liquid,  water  still  has  the  force  of  cohesion, 
the  force  of  holding  its  molecules  together,  so  that  the  water 
stays  in  a  body  and  remains  in  the  bottom  of  a  vessel. 

When  the  liquid  changes  to  a  gas  or  vapor,  the  molecules, 
being  much  farther  apart,  do  not  attract  one  another  per- 
ceptibly, but  fly  as  far  apart  as  the  containing  vessel  allows 
them  to  go.  The  energy  needed  to  tear  them  apart  is  the 
heat  we  supply  in  boiling  the  water. 

The  amount  of  heat  necessary  to  change  a  unit  weight  of  a 
liquid  to  a  gas  without  changing  its  temperature  is  called  its 
heat  of  vaporization. 

The  heat  of  vaporization  of  water  is  the  amount  of  heat 
necessary  to  change  1  pound  of  water  to  steam  without  chang- 
ing its  temperature.  This  has  been  found  to  be  966  B.  T. 
U.'s  per  pound.  (English  system.) 

Or,  the  heat  of  vaporization  of  water  is  the  amount  of  heat 
necessary  to  change  1  gram  of  water  to  steam  without  chang- 
ing its  temperature.  This  has  been  found  to  be  537  calories 
per  gram.  (Metric  system.) 

When  water  vapor  or  steam  condenses,  it  gives  up  the 
same  amount  of  heat  as  was  taken  in  to  vaporize  it,  that  is, 
537  calories  per  gram,  or  966  B.  T.  U.'s  per  pound. 

The  heat  of  vaporization  has  many  applications  in  steam 
heating  of  houses,  effect  on  climate  near  a  large  body  of 
water,  steam  cookers,  double  boilers,  etc. 

18.  Steam  Heating  of  Houses.  —  Due  to  the  great  heat 
t>f  vaporization  of  water,  steam  is  very  commonly  used  for 


STEAM   HEATING  OF  HOUSES 


17 


heating  buildings.  The  steam  is  sent  through  radiators  in 
the  rooms,  and  the  966  B.  T.  U.'s  per  pound,  absorbed  when 
the  water  was  changed  to  steam,  is  given  to  the  air  of  the 
room  when  the  steam  condenses  in  the  radiators. 


FIGURE  8.  —  A  STEAM-HEATING  SYSTEM. 

There  are  several  systems  of  steam-heating.  Figure  8 
shows  one  of  them.  This  is  called  the  one-pipe  system. 
The  steam  is  led  out  of  the  top  of  the  boiler  in  the  basement 
to  the  radiators  in  the  different  rooms.  Here  it  condenses, 


18 


HEAT   AND    HEAT    MEASUREMENT 


gives  off  its  heat,  and  the  condensed  water  runs  back  down 
the  same  pipe. 

To  get  the  steam  into  the  radiator  at  the  start,  the  little 
stop-cock  at  the  top  of  the  radiator  should  be  opened  in 
order  that  the  air  may  get  out  and  the  steam  take  its  place. 
After  the  radiator  is  full  of  steam  the  valve  can  be  closed, 
and  as  fast  as  the  steam  condenses  new  steam  will  flow  up 
and  take  its  place.  Some  radiators  have  stop-cocks  which 

are  open  when  the  radi- 
ators are  cold,  but  close 
automatically  when 
heated  by  the  steam. 
19.  The  Steam  Cooker. 
-  The  steam  cooker 
(Figure  9)  is  a  closed 
box  with  shelves.  It  is 
partly  filled  with  water 
and  set  on  the  stove,  or 
directly  attached  to  a 
stove  with  a  separate 
burner.  When  the  water 
boils,  the  steam  fills  the 
space  about  the  food  on 
the  shelves.  This  hot 
steam  cooks  the  food, 

without    danger    of    burning.     The    steam    cooker    is    well 
adapted  for  cooking  puddings,  custards,  etc. 

20.  The  Double  Boiler.  —  The  double  boiler  is  a  com- 
bination of  two  vessels.  (Figure  10.) 

The  smaller,  containing  the  food  to  be  cooked,  is  set  in- 
side a  larger  vessel,  partly  filled  with  water.  The  food  can 
be  cooked  for  a  long  time  and  cannot  burn  as  long  as  there 


FIGURE  9.  —  A  SIMPLE  STEAM  COOKER. 


DISTILLATION 


19 


FIGURE  10.  —  LINE  DRAWING  OF  A 
DOUBLE  BOILER. 


is  water  in  the  outer  vessel.     The  temperature  never  rises 
above  100°  C.  or  212°  F. 

21.  Distillation.— Theques- 
tion  of  pure  drinking  water  is 
of  vital  importance,  especially 
in  large  cities.  Sometimes 
chlorine  is  put  into  the  water 
to  kill  the  germs.  As  chlorine 
is  very  distasteful  to  some 
people,  they  prefer  to  buy,  or 
prepare,  distilled  water. 

The  process  consists  of  boil- 
ing the  water,  converting  it 
into  steam,  and  then  con- 
densing this  steam,  thus  pro- 
curing pure  water.  Figure  12  shows  the  principle  used 
even  in  large  establishments. 

Water  is  heated  in  a  boiler  (B),  and  the  steam  is  conducted 
through  a  pipe  to  a  coil  (C),  in  a  tank  of  running  cold  water. 

The  cold  water  is  supplied 
by  a  hose  from  the  city 
water  main  to  the  point  a, 
and  when  warmed  flows 
out  of  the  opening  b  into 
the  sewer  or  into  a  tank. 
The  steam,  passing  through 
the  coil,  is  condensed,  giving 
up  its  966  B.  T.  U.'s  per 
pound  to  the  cold  water, 
and  then  runs  out  of  the  coil 
as  pure  water.  It  is  pure  because  only  the  water  will  evapo- 
rate ;  hence  only  pure  water  vapor  is  in  the  coil  to  condense. 


FIGURE  11.  —  PHOTOGRAPH  OF  AN 
ALUMINUM  DOUBLE  BOILER. 


20 


HEAT   AND   HEAT    MEASUREMENT 


Distillation  is  used  to  refine  other  substances,  such  as 
alcohol  and  turpentine.  But  in  these  cases  the  substance 
has  to  be  distilled  several  times,  and  the  process  is  then 
called  fractional  distillation. 

In  the  case  of  alcohol,  the  liquid  which  contains  the 
alcohol  is  placed  in  a  boiler  and  heated,  the  temperature 


FIGURE  12.  —  DIAGRAM  OF  A  SIMPLE  DISTILLATION  SYSTEM. 

being  kept  at  the  boiling  point  of  alcohol,  which  is  below 
the  boiling  point  of  water.  The  alcohol  vapor  is  driven  off, 
but  with  it  a  little  water  evaporates.  When  this  is  con- 
densed again,  it  still  contains  some  water.  This  new  liquid 
is  again  distilled,  yielding  a  product  more  nearly  pure  alcohol. 
This  process  is  kept  up  until  the  liquid  is  as  nearly  pure  as 
desired. 


ARTIFICIAL  ICE  PLANT  21 

22.  Other   Applications    of   Heat    of   Vaporization.  —  In 

the  summer  time,  regions  far  inland  get  very  warm.  But 
near  a  large  body  of  water  the  heat  is  less  intense  because, 
in  evaporating,  the  water  takes  up  966  B.  T.  U.'s  for  every 
pound  evaporated;  and  thus  keeps  the  temperature  lower 
than  it  would  otherwise  be. 

You  have  probably  noticed  that  the  air  gets  cooler  after 
you  have  sprinkled  the  street  or  lawn.  The  water  on  the 
ground  begins  to  evaporate,  taking  heat  from  the  ground 
and  air,  thus  lowering  the  temperature.  The  same  thing 
occurs  after  a  rain. 

Nature  uses  the  same  principle  to  keep  your  body  cool. 
When  you  exert  yourself  strenuously,  or  when  the  day  is 
warm,  perspiration  is  thrown  out  to  the  surface  by  the  skin. 
This  perspiration  evaporates,  taking  the  heat  from  the 
body  to  do  it.  Would  you  get  as  cool  if  you  removed  the 
drops  with  your  handkerchief? 

23.  Artificial  Ice  Plant.  —  In  making  artificial  ice,  the 
same  principles  apply  as  in  natural  evaporation  and  freezing. 
The  ice  freezes  as  naturally  as  the  ice  on  a  lake.     The  only 
artificial   part  is  the   producing   of  the   low  temperature. 
Nature  does  the  rest. 

The  artificial  ice  plant  (Figure  13)  consists  of  four  prin- 
cipal parts:  a  cooling  coil  (A)  for  the  ammonia  gas;  a 
force  pump  (P)  for  compressing  the  ammonia  gas;  an 
expansion  coil  (B)  where  the  brine  cools;  and  a  freezing 
tank  (C)  where  the  ice  is  frozen. 

The  operation  of  the  plant  is  as  follows :  the  force  pump 
P  draws  the  ammonia  gas  through  the  valve  d  and  forces 
it  through  the  valve  e,  under  high  pressure.  From  here  it 
is  led  through  the  coils  in  the  tank  (^4),  where  it  is  cooled 
by  running  cold  water. 


22 


HEAT   AND   HEAT   MEASUREMENT 


As  the  gas,  under  high  pressure,  becomes  cool,  it  con- 
denses and  is  led  out  of  the  coil  at  the  bottom  as  liquid 
ammonia.  At  the  stop-cock  /  the  liquid  is  allowed  to  flow 
through  slowly,  and  there  it  turns  to  a  gas  and  expands  sud- 
denly. This  evaporation  and  expansion  require  a  great 
amount  of  heat. 

As  this  evaporation  and  expansion  take  place  in  the  coil 
in  the  tank  (B),  the  heat  is  taken  from  the  brine  in  tank  (B), 


FIGURE  13.  — DIAGRAM  OF  A  SIMPLE  ARTIFICIAL  ICE  PLANT. 

thus  reducing  its  temperature  several  degrees  below  0°  C. 
or  32°  F.  The  ammonia  gas  then  passes  on  up  to  the  force 
pump,  to  be  again  compressed  and  used  over.  The  cold 
brine  is  pumped  from  tank  (B)  to  tank  (C).  In  (C)  are 
placed  the  molds  containing  pure  water.  The  heat  passes 
from  the  water  to  the  brine,  and  thus  the  water  freezes. 

In  iceless  refrigerators  cold  brine  is  pumped  through 
coils  just  as  in  the  artificial  ice  plant.  Modern  meat  mar- 
kets use  this  method. 

The  ice  in  artificial  ice  skating  rinks  is  frozen  by  the  n  ethod 


WATER    VAPOR   IN   THE   AIR  23 

above.  Coils  of  pipe  are  placed  on  the  bottom  of  the 
floor,  and  then  enough  water  is  run  over  it  to  cover  these 
pipes  an  inch  or  two.  Brine  is  pumped  through  the  pipes, 
which  in  turn  freezes  the  water.  In  this  way  ice  skating 
can  be  had  at  any  time  of  the  year. 

Problems 

1.  Find  the  heat  required  to  evaporate  two  pounds  of  water  with- 
out changing  its  temperature. 

2.  Find  the  heat  required  to  evaporate  1500  grams  of  water  with- 
out changing  its  temperature. 

3.  If,  in  making  jelly,  one  half  of  the  weight  of  the  juice  is  boiled 
away,  how  much  heat  is  required  to  make  one  quart  of  jelly  ?     (Take 
weight  of  juice  as  eight  pounds  per  gallon,  and  starting  temperature 
as  62°  F.) 

4.  When  ten  pounds  of  steam  is  condensed  in  your  radiator,  how 
much  heat  is  given  to  the  room  ? 

24.  Water  Vapor  in  the  Air.  —  When  water  is  boiled 
away  in  a  tea-kettle  or  a  pan,  or  when  it  evaporates  from 
any  body  of  water,  the  water  seems  to  disappear;  but  it 
does  not  go  out  of  existence.  It  simply  goes  into  the  air 
and  is  invisible.  The  molecules  of  water  vapor  mix  with 
the  molecules  of  other  substances  in  the  air,  of  which  they 
become  a  part. 

There  is  a  limit  to  the  amount  of  water  vapor  that  the 
air  will  hold,  and  this  limit  depends  upon  the  temperature 
of  the  air.  The  warmer  the  air,  the  more  vapor  it  will 
hold. 

When  the  air  contains  all  the  water  vapor  it  will  hold,  it 
is  said  to  be  saturated,  or  to  have  reached  the  saturation 
point.  The  saturation  point  depends  upon  the  temperature. 

The  following  table  shows  the  vapor  tension  of  water 
under  normal  pressure  at  different  temperatures. 


24 


HEAT   AND   HEAT    MEASUREMENT 


TEMPERATURE 

VAPOR  TENSION 
(cm.  of  mercury) 

TEMPERATURE 

VAPOR  TENSION 
(cm.  of  mercury) 

o°c. 

0.460 

21°  C. 

1.862 

16°  C. 

1.362 

22°  C. 

1.979 

17°  C. 

1.440 

23°  C. 

2.102 

18°  C. 

1.546 

24°  C. 

2.232 

19°  C. 

1.645 

25°  C. 

2.36£- 

20°  C. 

1.751 

100°  C. 

76.000 

25.  The  Hygrometer.  —  An  instrument  used  to  measure 
the  amount  of  water  vapor  in  the  air  is  called  a  hygrometer. 
Figure  14  shows  a  common  form  of  the  hygrometer.  It 
consists  of  a  small  spring,  a  pointer,  and  a  scale.  The  scale 

denotes  the  per  cent 
of  water  vapor  in  the 
air,  complete  satura- 
tion being  100  per 
cent.  For  example,  a 
reading  of  65  per  cent 
means  that  there  is 
65  per  cent  as  much 
water  vapor  in  the  air 
as  it  would  hold  if 
saturated. 

By     knowing     the 
weight    of    vapor    re- 
FIGURE  14.  — THE  HYGROMETER.  quired    at    a    certain 

temperature  to  satu- 
rate the  air,  with  the  hygrometer  reading  it  is  easy  to  com- 
pute the  exact  weight  of  vapor  that  is  in  the  air. 

If  saturated  air  is  heated  to  a  higher  temperature,  it  will 
hold  more  vapor ;  but  if  saturated  air  is  cooled  it  will  hold 
less,  and  some  of  the  vapor  must  condense. 


SNOW  AND   HAIL  25 

26.  Dew.  —  If  warm  air  comes  in  contact  with  a  cold 
object  it  may  be  cooled  below  the  saturation  point  and  some 
of  its  water  vapor  may  condense  and  appear  as  drops  on 
the  cold  object.     These  drops  are  called  dew.     You  have 
all  seen  a  pitcher  of  ice  water  sweat  in  the  summer  time. 
The  pitcher  does  not  really  sweat,  but  merely  has  dew  on  it. 

Dew  also  forms  on  grass  and  on  the  leaves  of  trees.  During 
the  night  small  objects,  such  as  the  grass  blades  and  leaves, 
radiate  their  heat ;  and  thus  become  cooler  than  the  surround- 
ing objects.  These  grass  blades  and  leaves  then  cool  the 
air  that  touches  them,  and  dew  forms  when  the  air  is  moist. 

27.  Fog  and  Clouds.  —  If  a  cool  current  of  air  strikes  a 
warm  current,  the  warm  air  is  cooled  below  the  saturation 
point,  and  the  surplus  water  vapor  condenses,  in  very  small 
particles,  but  large  enough  to  be  visible.     If  this  condensa- 
tion occurs  near  the  surface  of  the  earth,  it  is  called  fog. 
If  it  occurs  high  in  the  air,  it  is  called  clouds.     The  greatest 
fog  region  in  the  world  is  just  off  the  banks  of  Newfound- 
land, where  the  cold  air  from  the  north  meets  the  warm 
air  from  the  Gulf  Stream. 

28.  Mist  and  Rain.  —  If,  in  the  case  of  fog,  the  condensed 
particles  become  sufficiently  large  to  fall  slowly,  they  are 
called  mist.     If  these  particles  become  large  enough  to  fall 
rapidly,  they  become  drops  and  are  called  rain. 

29.  Snow  and  Hail.  —  When  the  water  vapor  is  forced  to 
condense  at  a  temperature  below  the  freezing  point,  the 
small   particles   freeze   as   they   condense   and   form   snow- 
flakes.     The  flakes  get  larger  and  larger  as  they  come  into 
contact  with  one  another  in  the  air. 

The  formation  of  hail  is  more  complex  than  that  of  the 
other  forms  of  condensed  water  vapor  we  have  noted. 
Scientists  are  not  entirely  agreed  as  to  the  facts  concerning 


26  HEAT   AND   HEAT   MEASUREMENT 

the  process.  The  theory  generally  accepted  is  that  a  small 
particle  of  water  is  condensed  and  frozen  high  up  in  the  air. 
It  starts  to  fall  and  collects  on  its  surface  a  layer  of  water ; 
but  before  it  hits  the  earth  it  is  carried  up  again  by  an  up- 
ward current  of  air.  This  water  freezes  on  its  surface, 
while  at  the  high  altitude,  forming  a  new  layer  of  ice.  Again 
it  starts  to  fall,  and  collects  a  new  layer  of  water,  only  to  be 
carried  up  again  by  another  upward  current.  This  process 
is  repeated  until  the  hail  stone  becomes  so  heavy  that  it 
cannot  be  carried  up  any  more. 

This  theory  of  formation  is  based  upon  the  structure  of 
a  hailstone.  When  cut  open,  it  is  found  to  be  made  up  of 
distinct  layers;  some  of  clear  ice  and  some  of  snow  ice. 

30.  Heat  Capacity.  —  If  you  heat  a  five-pound  flat-iron 
to  the  boiling  point,  and  place  it  in  a  pan  of  cold  water,  and 
if  you  then  pour  five  pounds  of  boiling  water  into  another 
pan  containing  an  equal  amount  of  equally  cold  water,  you 
will  find  that  the  five  pounds  of  boiling  water  have  made 
the  pan  into  which  it  was  poured  much  warmer  than  the 
flat-iron  has  made  the  pan  in  which  it  was  placed. 

What  conclusion  would  you  draw  from  this?  Note  that 
the  weights  of  the  boiling  water  and  the  hot  iron  were  the 
same;  that  they  were  at  the  same  temperature;  and  that 
they  were  put  into  the  same  weights  of  water,  which  were 
also  at  the  same  temperature.  The  answer  is,  the  water 
contained  more  heat  than  the  iron.  Different  substances 
hold  different  amounts  of  heat  at  the  same  temperature. 
In  other  words,  they  have  different  capacities  for  heat. 

The  definitions  of  our  heat  units  are  based  on  the  heat 
capacity  of  water.  We  say  that  when  1  gram  of  water  is 
heated  1°  C.,  a  calory  is  put  into  it ;  and  that,  if  1  pound  of 
water  is  heated  1°  F.,  a  B.  T.  U.  is  put  into  it. 


SPECIFIC  HEAT  27 

But  if  a  gram  of  any  substance  other  than  water  were  to 
be  heated  1°  C.,  it  would  not  take  exactly  1  calory,  but  a 
certain  fraction  of  a  calory,  depending  upon  the  substance. 

The  heat  capacity  of  a  substance  is  the  heat  required  to 
raise  a  unit  weight  of  the  substance  1°.  If  it  is  in  the  English 
system,  it  is  the  number  of  E.  T.  U.'s  required  to  raise  1 
pound  of  the  substance  1°  F. ;  if  it  is  in  the  metric  system, 
it  is  the  number  of  calories  required  to  raise  1  gram  of  the  sub- 
stance 1°  C. 

31.  Specific  Heat.  —  As  the  heat  capacity  of  pure  water 
is  uniform,  substances  having  different  heat  capacities  are 
compared  with  water  as  a  standard.  From  this  comparison 
we  get  the  term  specific  heat.  The  specific  heat  of  a  sub- 
stance is  the  ratio  of  the  heat  capacity  of  the  substance  to  the 
heat  capacity  of  pure  water. 

Eliminating  the  idea  of  heat  capacity,  we  can  define  specific 
heat  in  this  way :  Specific  heat  is  the  ratio  between  the  amount 
of  heat  necessary  to  raise  a  certain  weight  of  the  substance  1° 
and  the  amount  of  heat  necessary  to  raise  the  same  weight  of 
pure  water  1° ;  or 

Heat  to  raise  substance  1° 

specific  Heat  =  77 — — ; —      — ? .  ,      , — 73 

Heat  to  raise  equal  weight  oj  water  1 

Table  of  Specific  Heats  of  Some  of  Our  Most  Common  Substances 

SUBSTANCE  SPECIFIC  HEAT 

Aluminum 22 

Brass 094 

Copper 095 

Iron 1138 

Mercury 038 

Lead 031 

Ice 5 

Air  (at  constant  pressure) .2375 

Hydrogen  (at  constant  pressure) 3.4 

Steam  (at  constant  pressure) 48 


28  HEAT   AND   HEAT   MEASUREMENT 

32.  Application  of  Specific  Heat. —  The 
high  specific  heat  of  water  has  a  powerful 
effect  on  the  climate  of  regions  near  a  large 
body  of  water.  This  effect  is  the  same  as 
that  produced  by  the  high  heat  of  fusion. 
The  principle  is  slightly  different,  for  the  heat 
is  used  to  raise  the  temperature  of  the  water, 
instead  of  to  melt  the  ice.  (See  §  16.)  The 
effect  is  much  greater  than  it  would  be  if  the 
HO  WATER  body  were  mercury  or  alcohol  or  any  substance 
BOTTLE.  whose  specific  heat  is  less  than  that  of  water. 

The  hot  water   bottle   is   an   application   of   specific   heat. 

It  is  better  than  a  hot  flat-iron  or  other  hot  object,  not  only 

because  it  is  more  convenient,  but  also  because  it  holds  more 

heat. 


CHAPTER  II 
EXPANSION 

33.  Expansion.  —  One    effect    of   heat    is    to    make    the 
molecules  of  a  body  vibrate  faster.     This  increase  in  speed 
causes  the  molecules  to  take  up  more  space.     The  mole- 
cules themselves  do  not  get  any  larger,  but  they  require 
more  free  space  in  which  to  vibrate. 

Suppose  a  number  of  people  were  to  stand  close  together, 
with  a  large  rubber  band  stretched  around  the  whole  crowd. 
If  all  stood  perfectly  still,  they  could  get  into  a  compara- 
tively small  space.  But  if  every  one  began  swaying  and 
elbowing  his  neighbor,  each  person  would  take  up  more 
room,  and  consequently  the  space  occupied  would  be  larger, 
and  the  rubber  band  would  have  to  stretch. 

This  is  what  takes  place  when  a  body  is  heated ;  and  we 
call  it  expansion.  Expansion  is  the  increase  in  length  or 
volume  of  a  body. 

34.  Coefficient  of  Linear  Expansion.  —  All  substances  do 
not  expand  at  the  same  rate.     For  example,  a  bar  of  iron  a 
foot  long  would  not  expand  as  much  as  a  bar  of  brass  a 
foot  long,  if  both  were  heated  through  the  same  range  of 
temperature.     In  order  to  have  a  way  of  expressing  how 
much  a  substance  expands  we  use  the   term   coefficient  of 
linear  expansion. 

The  coefficient  of  linear  expansion  of  a  substance  is   its 
expansion  per  unit  length  per  degree  C. 

29 


30  EXPANSION 

Suppose  a  bar  of  aluminum,  60  cm.  long  at  25°  C.  (Figure 
10),  gets  .1  cm.  longer  when  heated  to  100°  C.     The  in- 
crease in  temperature 
from  25°  C.  to  100°  C. 


-60  cmr 


is  75°  C.     If  the  bar 
h— 1  cm.   exPands  .1  cm.  for  75° 


FIGURE  16.-  EXPANSION  OF  A  ROD. 


C.,  it  will  expand   ; 
/o 

cm.  for  1°  C.     If  60  cm.  expand  £7  cm.,  then  1  cm.  will 

7o 

expand  — ^—  cm.  or  7^  cm.  -  .000022  +cm. 

/  O  A  vJU  -±OUU 

The  number  .000022  is  called  the  coefficient  of  linear  ex- 
pansion of  aluminum. 

Table  of  Coefficients  of  Linear  Expansion 
SUBSTANCES  COEFFICIENT 

Aluminum 0000222 

Brass 0000187 

Copper 000017 

Glass .0000083 

Iron     .     .     .     .    -. 0000112 

Platinum 0000088 

Steel 000013       (tempered) 

Steel    .     .     . 000011       (untempered) 

If  the  range  in  temperature  is  given  in  F.  degrees,  then  the  above 
coefficients  must  be  multiplied  by  f . 

35.  The  Thermostat.  —  The  thermostat  which  regulates 
the  heat  of  our  rooms  uses  the  principle  of  expansion.  It 
is  constructed  as  shown  in  Figure  17.  The  pointer  (P)  is 
made  of  a  strip  of  steel  (<S)  and  a  strip  of  brass  (B),  laid 
side  by  side  and  fastened  so  that  they  cannot  slip  on  each 
other.  One  end  is  fixed,  and  the  other  end  is  free.  Electric 


THE   THERMOSTAT 


31 


connections  are  made  as  shown  in  the  figure.  The  battery 
(Bat.)  is  placed  in  the  circuit,  together  with  two  magnets 
(Mi  and  M2). 

The  thermostat  is  placed 
in  the  room,  the  temperature 
of  which  is  to  be  regulated, 
and  the  magnets  (Mi  and 
M2)  are  placed  in  the  base- 
ment. The  wires  lead  from 
the  thermostat  to  the  mag- 
nets. When  the  room  gets 


FIGURE  17.  —  DIAGRAM  OF  A  THERMO- 
STAT AND  SYSTEM. 

too  warm,  the  two  metals  ex- 
pand ;  but  the  brass  expands 
the  faster.  This  makes  the 
pointer  bend  and  touch  the 
connection  x,  thus  operating 
magnet  M2.  Magnet  M2  re- 
leases a  spring  which  closes 
the  draft  of  the  furnace,  and 
this  allows  the  room  to  cool. 
When  it  gets  cool  enough, 
the  two  metals  contract ;  but 
the  brass  one  contracts  the 
more.  This  makes  the  pointer 
bend  in  the  other  direction, 

and  it  touches  the  contact  point  y.     This  operates  magnet 
MI,  which  releases   a   spring  opening   the  draft.      In   this 


FIGURE  18.  —  PHOTOGRAPH  OF  THE 
SENSITIVE  PART  OF  A  THERMOSTAT. 


32 


EXPANSION 


way    a    room    may    be    automatically    kept    at    an    even 
temperature. 

36.  Compensating  Pendulum  of  a  Clock.  —  The  pendulum 
of  a  clock  is  the  regulator  which  makes  the  clock  run  evenly. 
If  the  pendulum  is  too  short,  the  clock  runs  too  fast;  and 
if  it  is  too  long,  it  runs  too  slowly. 

Since  metals  expand  when  heated,  a  clock 
will  not  run  correctly  at  different  tempera- 
tures unless  a  special  pendulum  is  arranged. 
When  a  pendulum  is  so  arranged  that  a 
change  in  temperature  does  not  affect  it,  it 
is  called  a  compensating  pendulum. 

One  kind  of  compensating  pendulum  is 
shown  in  Figure  20.  The  dark  lines  repre- 
sent rods  which  are  made  of  brass,  while  the 
other  ones  represent 
rods  of  steel.  By 
looking  at  the  figure 
you  will  see  that  the 
steel  rods  make  the 
pendulum  longer 
when  they  expand, 
and  the  brass  rods 
make  it  shorter  when 
they  expand.  The 
lengths  of  brass  and 
steel  are  so  calcu- 
lated that  whenever 
the  steel  rods  let  the 
bob  down  the  brass 
rods  lift  it  up  the 
FIGURE  19.  — A  THERMOSTAT  INSTALLED.  same  amount.  This 


BALANCE   WHEEL  OF  A    WATCH 


33 


keeps  the  pendulum  at  the  same  length,  regardless  of  the 
temperature.  Another  method  of  accomplishing  the  same 
thing  is  shown  in  Figure  21. 

The  pendulum  has  a  cup  at  the 
bottom,  containing  mercury.  As  the 
temperature  rises,  the  rod  of  the 
pendulum  becomes  longer ;  but  at 

the    same    time 

the  mercury  ex- 
pands and  rises 

in  the  cup,  thus 

counteracting 

the     expansion 

of  the  rod. 
37.    Balance 

Wheel     of     a 

Watch.  —  Good 

watches  have  to 

Jbe  so  made  that 

change  of  tem- 
perature      will 

not  affect  them.    FIGURE  20.  — A   COMPEN- 

rpi  i        i  SATING    PENDULUM    WITH 

The        balance        BRASS  AND  STEEL  RODS. 

wheel  is  to  the 

watch  what  the  pendulum  is  to  a 
clock.  If  the  wheel  gets  larger,  the 
watch  runs  more  slowly;  and  vice 
versa.  The  rim  of  the  wheel  (Figure 
22)  is  made  of  two  metals,  steel  and 
brass,  just  as  is  the  pointer  of  the 
thermostat.  The  brass  is  put  on  the 
A  MERCURY  WELL.  outside  of  the  rim ;  so  that,  whea 


34 


EXPANSION 


FIGURE  22.  —  BALANCE  WHEEL  OF 
A  WATCH. 


the  temperature  rises  and  the  spoke  gets  longer,  the  brass 

expands  faster  than  the  steel    and  makes   the   rim   curve 

more,  tending  to  make  the 
wheel  smaller.  These  two 
effects  exactly  counterbalance 
each  other,  and  so  the  watch 
keeps  even  time. 

38.  Hot  Water  Dangerous 
to  Glassware.  —  Each  of  us 
has  probably  broken  glass- 
ware by  putting  hot  water 
into  it.  Why  does  hot  water 
break  the  glass  into  which  it 
is  poured?  Unequal  expan- 
sion is  the  cause. 
As  the  water  goes  into  the  glass  the  inside  is  heated  first, 

and  so  expands ;   while  the  outside  does  not.     This  puts  the 

glass  under  a  great  stress,  and  so  it  breaks. 

You  feel  the  same  effect  in  your  teeth  when  you  take  a 

bite  of  ice  cream  or  drink  ice  water.     The  outside  of  the 

teeth  is  cooled  and  contracts  before  the  inside  can  cool  off; 

and  so  the  nerves  are  squeezed  under  a  high  pressure. 

If  glasses  are  put  into  a  pan  of  water  and  brought  slowly 

to  a  boil,  they  will  not  break;    nor  will  a  very  thin  glass 

break  as  easily  as  a  thick  one  when  filled  with  hot  water. 

Explain. 

When  glass  stoppers  stick,  they  can  often  be  gotten  out 

of  bottles  by  applying  a  flame  to  the  neck  of  the  bottle  for 

a  short  time.     This  causes  it  to  expand  and  so  loosens  the 

stopper. 

Thrusting  the  neck  of  the  bottle    into  warm  water  will 

produce  the  same  result. 


EXPANSION  EFFECTS   WHEN   WATER  IS  HEATED    35 

39.  Coefficient  of  Cubical  Expansion.  —  When  a  body  is 
heated,  it  gets  larger  in  every  direction.     Therefore  it  has 
more  volume.     This  increasing  in  volume  is  called  volume 
expansion.    The    coefficient    of   volume    expansion   is    the 
increase  in  volume  per  degree  C.,  per  unit  volume. 

Since  a  body  expands  in  three  directions,  its  coefficient 
of  volume  expansion  is  approximately  three  times  its  coeffi- 
cient of  linear  expansion. 

For  example :  What  is  the  increase  in  volume  of  1000  cubic  centi- 
meters of  aluminum  for  a  range  of  50°  C.  ? 

The  coefficient  of  linear  expansion  for  aluminum  is  .000022 ;    so  the 
coefficient  of  volume  expansion  is  .000022  X  3  =  .000066. 
Then  1000  X  .000066  X  50  =  3.3  c.c. 
Therefore  the  1000  c.c.  of  aluminum  will  increase  3.3  c.c. ; 
or  will  then  contain  1000  +  3.3  =  1003.3  c.c. 

Problems 

1.  Find  the  increase  in  length  of  an  aluminum  bar  60  cm.  long 
when  it  is  heated  from  22°  C.  to  100°  C. 

2.  If  an  iron  steam  pipe  leading  from  the  boiler  in  the  basement 
to  an  upper  story  room  is  120  ft.  long,  and  20°  C.,  how  much  will  it 
expand  when  steam  at  100°  C.  is  passed  through  it? 

3.  Will  the  lids  fit  tighter  when  the  stove  is  hot  or  when  it  is  cold? 
Why? 

4.  If  the  pointer  of  a  thermostat  is  2"  long,  and  is  made  of  brass 
and  steel,  what  is  the  difference  in  length  of  the  brass  and  steel  when 
it  is  heated  10°  C.  ? 

5.  How  much  will  a  copper  wire  10  ft.  long  expand  in  length  if 
heated  from  60°  F.  to  180°  F.  ? 

6.  How  much  will  6000  c.c.  of  brass  expand  when  heated  from 
32°  F.  to  212°  F.  ? 

7.  Will  a  glass  flask  hold  more  when  hot  or  cold  ?     Why  ? 

40.  Peculiar  Expansion  Effects  when  Water  is  Heated.  — 
Nearly  all  of  our  common  substances  expand  when  heat  is 


36  EXPANSION 

applied,  regardless  of  their  state  and  temperature.  For 
example  a  piece  of  iron  will  expand  when  heated ;  and  when 
it  melts,  it  still  expands;  and  when  the  molten  metal  is 
heated,  it  still  expands;  and  likewise  when  it  is  vaporized 
and  the  gas  is  heated.  Expansion  takes  place  whenever 
heat  is  applied. 

But  there  is  an  exception  to  this  rule.  The  exception  is 
when  ice  is  melting,  and  when  the  water  is  heated  from 
0°  C.  to  4°  C. 

If  a  piece  of  ice  at  a  temperature  below  0°  C.,  say  — 10°  C., 
is  heated,  its  temperature  rises  to  0°  C.,  and  the  ice  increases 
in  volume.  Then,  if  more  heat  is  applied,  the  ice  melts,  the 
temperature  remaining  at  0°  C. ;  but  the  volume  decreases. 
After  it  is  all  melted,  the  temperature  again  rises ;  and  until 
4°  C.  is  reached,  the  water  still  contracts.  After  4°  C.  is 
reached,  the  temperature  continues  to  rise  to  100°  C.,  but 
the  water  expands.  At  100°  C.  the  water  changes  to  steam, 
the  temperature  remaining  at  100°  C.  until  it  is  all  steam ; 
and  the  volume  increases  to  about  1650  times  its  former 
volume.  If,  after  the  water  is  all  steam,  it  is  still  heated 
at  constant  pressure,  the  temperature  increases,  and  the 
gas  expands. 

The  best  way  to  remember  all  this  is  to  keep  in  mind 
that  water  is  like  all  other  common  substances  and  expands 
when  heated,  except  when  melting  and  being  raised  from 
0°  C.  to  4°  C. 

41.  Importance  of  4°  C.,  the  Temperature  at  which  Water 
is  Densest.  —  Did  you  ever  think  why  the  rivers  and 
lakes  freeze  on  top  instead  of  at  the  bottom?  The  reason 
is  that  water  is  densest,  —  or,  in  other  words,  heaviest, 
per  cubic  unit, —  at  4°  C. 

In  the  summer  time  the  temperature  of  the  water  may 


WHY   WATER  PIPES  BURST  37 

reach  18°  C.  or  20°  C.  As  the  weather  gets  cooler  in  the 
fall,  the  top  layers  of  water  are  cooled  by  the  air.  They 
are  then  heavier  than  the  layers  below  them ;  so  they  sink 
until  they  come  to  water  as  cool  as,  or  cooler  than,  they  are. 
This  leaves  exposed  to  the  air  a  new  layer  which  in  turn 
cools  and  sinks. 

This  displacement  is  kept  up  until  the  whole  body  of 
water  is  cooled  to  4°  C.  Then,  when  the  top  layer  gets 
colder  than  4°  C.  it  expands,  and  becomes  lighter  than  the 
water  below  it ;  therefore,  it  remains  on  top,  continuing  to 
get  colder  and  lighter.  When  it  reaches  0°  C.,  it  freezes 
and  expands  still  more.  This  ice  layer  protects  the  un- 
frozen water,  which  remains  at  4°  C.,  except  for  the  layers 
next  the  ice. 

If  water  were  like  mercury  and  continued  to  contract  as  it 
cooled,  large  bodies  of  water  would  freeze  solid  in  cold 
weather.  The  water  would  cool  at  the  top  and  sink,  letting 
the  warmer  water  come  to  the  surface.  This  would  con- 
tinue till  all  the  water  was  at  the  freezing  point,  when  the 
top  would  begin  to  freeze.  Then  the  ice  would  sink ;  and 
the  lakes  and  rivers  would  be  frozen  from  the  bottom  up. 
In  a  cold  winter  they  would  be  a  mass  of  solid  ice. 

Then  in  the  summer  the  ice  would  melt  only  on  top, 
leaving  the  lake  almost  a  solid  cake  of  ice.  The  result 
would  be  a  climate  too  cold  for  vegetable  life. 

42.  Why  Water  Pipes  Burst.  —  When  water  is  allowed 
to  remain  in  the  water  pipes  in  very  cold  weather,  it  freezes 
and  expands,  thus  breaking  the  pipes.  The  ice  acts  as  a 
plug  in  the  pipe,  otherwise  the  expansion  would  force  the 
water  back  into  the  water  mains,  in  which  case  the  pipes 
would  not  break.  It  is  because  the  water  is  imprisoned  in 
the  pipe  behind  the  ice  plug  that  the  pipe  must  give  way. 


38  EXPANSION 

43.  Expansion  of  Gases.  —  We  found,  from  our  study  of 
expansion  of  liquids  and  solids,  that  they  all  expand  at  a 
different   rate,   making    it    necessary   to    have    a    table   of 
coefficients    of    expansion.      In    the    case     of    gases    this 
is  different,,  all  gases  expanding  at  the  same  rate.     There- 
fore   there    is    only   one   coefficient    of   expansion   for   all 
gases. 

If  a  certain  volume  of  gas  be  heated  1°  C.,  it  will  expand 
-2T3  of  its  volume  at  0°  C.,  if  kept  at  the  same  pressure. 
This  fraction,  g-fs-,  or  -00366,  is  the  coefficient  of  expansion 
of  gases. 

If  273  c.c.  of  oxygen,  hydrogen,  air,  or  any  other  gas, 
were  heated  from  0°  C.  to  1°  C.,  the  gas  would  expand 
•JT-J  of  273  c.c.  =  1  c.c.  Therefore  the  same  amount  of 
gas  would  fill  a  vessel  of  274  c.c.  at  the  new  temperature, 
the  pressure  remaining  the  same. 

44.  Absolute  Zero.  —  Gases,  like  all  substances,  are  com- 
posed of  molecules;    but  under  normal  pressure  and  tem- 
perature  the   molecules   are   comparatively   far   apart.     It 
has  been  said  that  if  the  molecules  of  a  gas,  such  as  ordinary 
air,  were  magnified  until  they  were  the  size  of  an  orange, 
each  molecule  would  be  surrounded  by  a  space  equal  to  a 
cubic  yard.     If  this  is  true,  the  space  actually  taken  up 
by  the  molecules  is  very  small,  and  the  empty  space  about 
them  is  large. 

When  heat  is  applied,  each  molecule  flies  faster  than 
usual,  bumping  its  neighbors  farther  apart,  thus  making 
the  space  about  it  larger.  If  the  gas  is  cooled,  the  mole- 
cules move  more  slowly  than  usual ;  and  consequently  come 
closer  together.  The  more  the  gas  is  cooled,  the  more  slowly 
the  molecules  move,  until,  theoretically,  they  come  to  rest. 
There  is  then  absolutely  no  heat  in  the  gas.  When  at  rest 


SOME  APPLICATIONS  OF   CHARLES'   LAW          39 

they  occupy  so  little  space  that  it  is  not  counted  at  all; 
and  the  gas  is  said  to  have  no  volume. 

The  temperature  at  which  a  gas  has  no  volume  is 
—  273°  C.  This  temperature  is  then  called  absolute  zero, 
because  it  means  total  absence  of  heat. 

45.  Charles'   Law.  —  A   man   by   the   name   of   Charles 
formulated  a  law  about  the  expansion  of  gases.     This  is 
called  Charles'  Law : 

"  The  volume  of  a  gas  at  constant  pressure  is  proportional 
to  its  absolute  temperature" 

Example :  What  is  the  volume  of  a  gas  at  70°  C.,  if  it 
occupies  800  c.c.  at  20°  C.  ? 

Solution  :  The  original  absolute  temperature  is  20  +  273  =  293° ;  and 
the  final  absolute  temperature  is  70  +  273  =  343°.  Since,  by  Charles' 
Law,  the  volume  of  a  gas  is  proportional  to  its  absolute  temperature, 
the  new  volume  is  ftf  of  800  c.c.  =  936.5  +  c.c.,  or 

7  new  absolute  temperature  ^,      .  .     ,      , 

new  volume  = —  X  original  volume. 

old  absolut :  temperature 

46.  Some  Applications  of  Charles'  Law.  —  The  expansion 
of  gases  has  much  to  do  with  the  baking  of  bread,  cake,  or 
pie. 

To  make  bread,  yeast  is  used  to  produce  the  rising.  The 
dough  is  mixed  and  allowed  to  stand  in  a  warm  place.  The 
yeast  plants  grow  and,  in  growing,  give  up  carbon  dioxide 
gas.  The  dough  does  not  allow  this  gas  to  escape;  so  it 
forms  bubbles  in  the  dough,  causing  it  to  rise.  The  dough 
is  then  "  worked  down,"  and  again  allowed  to  rise  in  the 
same  way.  Usually  it  is  "  worked  down  "  a  second  time 
and  again  allowed  to  rise.  When  it  has  risen  properly,  it 
is  placed  in  a  hot  oven  and  baked. 

Up  to  this  time  the  rising  has  been  caused  by  the  growing 
yeast  plants.  But  when  it  is  put  into  the  oven,  the  heat 


40  EXPANSION 

kills  the  yeast  plants;  so  the  rising  after  that  is  due  to 
something  else.  The  carbon  dioxide  bubbles  in  the  dough 
are  heated.  According  to  Charles'  Law,  they  expand  -^TS 
of  their  volume  at  0°C.  for  every  degree  Centigrade  they  are 
raised  in  temperature.  This  makes  the  bread  rise  while 
it  is  baking. 

In  baking  biscuits  and  cakes,  baking  powder  is  used 
instead  of  yeast.  But  the  action  is  the  same.  Baking 
powder,  when  wet,  gives  off  carbon  dioxide.  The  rising 
takes  place  as  in  the  case  of  the  yeast.  Expansion  also 
takes  place  when  the  cake  or  biscuits  are  placed  in  the  oven. 

In  making  pie  crust  there  is  usually  nothing  put  into  the 
dough  to  make  it  rise.  But  the  crust  must  rise  a  little ;  or 
else  it  will  be  tough,  instead  of  brittle  and  flaky.  The  ex- 
pansion of  gases  is  used  to  produce  this  rise.  In  mixing, 
the  dough  should  be  worked  very  lightly  and  the  flour 
should  be  sifted  in.  Doing  this  gets  air  into  the  dough, 
and  the  light  working  leaves  it  there.  Then  if  the  dough 
is  chilled  by  placing  it  in  the  refrigerator,  the  open  spaces 
will  fill  up  with  cold  air.  This  cold  air  will  expand  when 
the  pie  is  baked,  producing  a  brittle,  flaky  crust. 

On  the  other  hand,  in  clay  modeling  care  is  taken  to  work 
all  the  air  out.  The  clay  is  kneaded  and  pounded  and 
squeezed  so  that  no  air  is  left  in  it.  If  the  air  is  not  all  out, 
when  the  piece  is  fired  in  the  kiln  these  bubbles  expand  and 
break  the  piece  of  pottery. 

Other  applications  of  the  expansion  of  gases,  which  will 
be  studied  under  another  topic,  are :  the  draft  in  a  stove, 
grate,  furnace,  chimney,  range;  hot-air  heating;  and 
ventilation. 


CHAPTER  III 
HEAT   TRANSFERENCE 

47.  Transference   of  Heat.  —  Heat   is   transferred   from 
one  place  to  another  by  three  methods,  conduction,  convection, 
and  radiation.     Each  of  these  will  be  taken  up  in  detail. 

48.  Conduction.  —  If  heat  is  applied  to  one  part  of  a 
body,  the  molecules  will  be  set  into  rapid  vibration  at  that 
point.     These    molecules    strike    their    neighbor    molecules 
and  set  them  in  vibration.     These  in  turn  set  the  next  ones 
going,  and  the  heat  travels  along  the  body  by  conduction. 

If  one  end  of  a  poker  is  placed  in  the  fire,  that  end  gets 
hot,  and  all  the  rest  of  the  poker  is  warmed.  But  the 
temperature  is  lower,  the  farther  away  from  the  end  in  the 
fire. 

Different  materials  conduct  heat  at  different  rates.  Those 
that  conduct  it  very  readily  are  called  good  conductors. 
Those  that  do  not  conduct  heat  readily  are  poor  conductors, 
or  are  good  insulators.  Silver,  copper,  gold,  aluminum,  iron, 
and  nearly  all  other  metals  are  good  conductors.  Among 
the  poor  conductors,  or  good  insulators,  are  asbestos,  a 
vacuum,  air  space,  water,  paper,  wood,  glass,  cloth,  por- 
celain, horn,  and  ivory. 

49.  Non-conducting   Handles   for    Cooking    Utensils.  - 
Figures  23,  24,  25,  and  26  show  different  methods  used  to 
keep  the  handles  of  cooking  utensils  cool.     The  teakettle 
is  made  of  metal,  all  except  the  handle,  and  that  is  made 

41 


42 


HEAT    TRANSFERENCE 


of  wood.     The  metal  becomes  hot  by  conduction,  but  the 
wood  does  not  let  the  heat  through. 

The  coffee-pot  and  the  percolator  have  handles  of  wood, 
porcelain,  horn,  or  ivory,  for  the  same  reason.     The  stove- 

poker     has      a      metal  Porcelain,  Horn  or  Ivory 

handle,  but  it  consists 


Wood 


FIGURE  23.  —  WOOD  HANDLES 
ON  A  TEA-KETTLE. 


FIGURE  24. — THE  HANDLES  OF  THE 
COFFEE-POT  ARE  INSULATED. 


Horn  or  Wood 


lass 


of  a  wire  wound   in  a  coil  about  the  end  of  the  poker. 

This   allows   air   space    between   the   poker   and   the  wire 

handle,  and  this  air  space  is  a  good  insulator. 

50.   Good  Conductor  Bottoms  on  Utensils.  —  The  bottoms 

of  coffee-pots,  tea-kettles,  wash-boilers,  etc.,  are  usually  of 

copper.  This  is  for  two 
reasons.  First,  copper  will 
not  corrode  as  readily  as  iron 
or  tin;  and  therefore  will 
keep  cleaner  and  last  longer. 
Second,  copper  is  a  good  con- 
ductor, so  that  the  heat  is 
readily  conducted  from  the  gas 

FIGURE  25.  -  INSULATION  FOR  THE     flame  or  from  the  stove  toP  to 
HANDLES  OF  A  PERCOLATOR.          the  contents  of  the  utensil. 


THE   FIRELESS   COOKER 


43 


Coil  of  Wire 


51.  The  Fireless  Cooker.  —  The  fireless  cooker  is  a  box 
arrangement  with  non-conducting  walls.  Figure  27  shows 
how  it  is  constructed. 
On  the  inside  are  pails  in 
which  the  food  is  placed. 
Around  the  pails  is  the 
non-conducting  wall.  The 
food  is  first  heated  to  the 
boiling  point,  and  at  the 
same  time  slabs  of  soap 
stone  or  iron  are  heated. 
When  these  are  hot 
enough,  the  hot  food  is  placed  in  the  pails  between  the 
hot  slabs ;  then  the  whole  box  is  closed  up  tight. 

The  non-conducting  walls  keep  the  heat  in,  so  that  the 
food   stays   up   close   to   the   boiling   temperature   without 


FIGURE  26. — -COILED  WIRE  HANDLE  ON 
A  STOVE-POKER. 


Pail  of  Food 


Hot  Plate 
Wood 

Felt 

Asbestos 

' Enamel  Ware 
^Mineral  Wool 

FIGURE  27. —  THE  FIRELESS  COOKER. 


being  supplied  with  more  heat.  This  makes  it  necessary 
to  use  the  fire  only  long  enough  to  get  the  food  and  heating 
slabs  hot. 


44 


HEAT    TRANSFERENCE 


The  non-conducting  material  used  may  be  wool,  felt, 
mineral  wool,  asbestos,  leather,  paper,  straw,  shavings,  or 
sawdust. 

52.  The  Refrigerator.  —  The  refrigerator  (Figure  28) 
uses  non-conducting  substances  for  its  walls.  On  the  out- 
side is  usually  wood ;  next  is  an  insulating  layer  of  paper ; 
then  another  of  wood ;  then  a  layer  of  asbestos  or  felt ; 
and  then  an  air  space.  The  inside  material  is  usually  glass, 


Glass  or 
Enamel  Ware- 

Air  Space 


7 


Mineral  Wool  or  Felt 

Rough  Wood 
Paper  or  Asbestos 
Finished  Wood 


FIGURE  28.  —  THE  CROSS  SECTION  OF  A  REFRIGERATOR  WALL. 

enamel,  or  zinc.  The  ice  is  put  into  the  top  of  the  refrigera- 
tor, and  the  things  to  be  kept  cool  on  the  shelves  below  or 
beside  it.  The  insulating  walls  allow  little  heat  to  come 
in  from  the  outside ;  so  that  most  of  the  heat  used  to  melt 
the  ice  comes  from  the  articles  put  in  to  be  cooled. 

53.  The  Thermos  Bottle.  —  The  thermos  bottle  consists 
of  a  double  glass  flask  with  the  outside  silver-coated  (Figure 
29).  The  space  between  the  walls  of  the  flask  is  a  vacuum, 
the  air  having  been  pumped  out.  The  flask  is  then  placed 
inside  of  an  outer  cover,  which  is  either  silver  or  nickel 


WALLS  OF  HOUSES 


45 


plated.     An  air  space  is  left  between  the  outer  cover  and 
the  glass  flask. 

The  bottle  is  used  to  keep  liquids  either  cold  or  hot. 
When  cold  liquids  are  placed  in  it,  the  heat  is  kept  out  by 
the  insulating  walls;  and  if  hot  liquids  are  placed  in  it, 
the  insulating  walls  keep  the  heat  in. 

The  reasons  for  this  are  apparent.  First,  the  glass  walls 
of  the  flask  are  non-conductors,  and  do  not  permit  heat  to 
pass  through  them 
easily.  Then,  the 
vacuum  is  the  best 
non-conductor  there 
is.  Also,  the  air 
space  between  the 
outside  cover  and  the 


Air  Space 
Metal  Case 


Screw  Cap 
Cork 

Glass  Flask 
-Vacuum 


-Contents 


^Where  Glass  Flask 
Was  Sealed 


FIGURE  29.  —  CROSS  SECTION  OF  A 
THERMOS  BOTTLE. 


flask    helps    the    in- 
sulation.        Finally, 
the  silvered  and  nickled  surfaces  have  special  uses,  which 
will  be  discussed  under  the  subject  of  Radiation. 

Good  thermos  bottles  will  keep  coffee  too  hot  to  drink 
for  fifteen  hours.  Care  must  be  taken  to  have  the  liquid 
hot  when  it  is  placed  in  the  bottle. 

54.  Walls  of  Houses.  —  Walls  of  houses  are  so  con- 
structed that  they  do  not  allow  the  heat  to  pass  through 
them  readily.  Either  brick,  stone  or  lumber  is  used. 
The  lumber-made  house  is  constructed  as  shown  in 
Figure  30. 

First  is  put  up  studding,  which  is  about  two  inches  by 
four  inches.  On  the  outside  of  this  is  nailed  rough  lumber, 
called  sheathing.  Over  this  is  usually  tacked  heavy  paper, 
and  then  the  siding  or  weather-board.  Inside  the  studding 
the  plaster  lath  is  nailed,  and  then  the  plaster  is  spread 


46 


HEAT    TRANSFERENCE 


over  this.     This  constitutes  the  complete  wall,  except  for 
the  wall  paper  usually  placed  on  the  inside. 

Naming  the  insulating  layers  from  the  outside  inward, 
they  are,  weather-board,  heavy  paper,  sheathing,  air  space, 
plaster  lath,  plaster,  and  wall  paper. 


Studding 


Lath 


Plaster 


Wall  Paper 


Sheathing 


Paper 


Siding 


FIGURE  30.  —  CROSS  SECTION  OF  THE  WALL  OF  A  HOUSE. 

Sometimes  in  cold  countries  an  extra  set  of  lath  and 
plaster  is  put  in  between  the  studding,  making  also  an  extra 
air  space. 

55.  Clothes.  —  Winter  clothing  is  usually  made  of  non- 
conductors. We  wear  light  cotton  clothes  in  summer  and 
heavy  woolens  in  winter.  Why?  The  cotton  is  compact 
and  conducts  heat  readily,  while  the  wool  is  loose  in  con- 
struction, containing  many  air  spaces,  which  act  as  insulators. 
You  can  easily  tell  the  difference  between  cotton  and  wool 
by  dampening  the  thumb  and  finger  and  rolling  a  thread 
of  each  between  them.  The  cotton  will  pack  closely  to- 


CONVECTION 


47 


gether,  while  the  wool  will  spring  back  to  its  original  loose- 
ness. 

56.  Convection.  —  Convection  is  the  second  method  of 
transferring  heat.  In  conduction  we  learned  that  it  was 
the  heat  energy  only  that  moved  along.  In  convection, 
the  heat  passes  from  one  place  to  another  by  means  of 
material  bodies  carrying  it. 

Convection  can  best  be  understood  by  studying  the 
following  drawing.  Figure  31  shows  a  section  of  air  divided 
into  columns.  If  a  r , 


1 

I 

A 

T      I 
t      t 

t      t 

B 

1 
1 

1      t 

1 

U" 

- 

->  > 

;  t 

FIGURE  31.  —  DIAGRAM  SHOWING  HOW  CON 
VECTION  CURRENTS  ARE  SET  UP. 


fire  were  built  under 
column  A  BCD,  the 
air  would  be  heated 
and  would  conse- 
quently expand.  As 
the  air  cannot  push 
sidewise,  on  account 
of  the  other  columns 
of  air,  when  it  ex- 
pands it  must  push 
upward.  This  makes  this  column  higher  than  the  others; 
so  the  air  flows  outward  over  the  other  air  columns  at  the 
top,  as  indicated  by  the  arrows. 

Now  this  makes  the  columns  at  the  side  heavier  than 
the  middle  one ;  so  they  crowd  down,  forcing  some  of  the 
cold  air  under  the  middle  column,  as  indicated  by  the  ar- 
rows. This  air  will  then  be  heated,  will  expand,  and  be 
pushed  up  by  more  cold  air. 

So  the  process  goes  on;  the  cold  air  flowing  towards  the 
warm  area  at  the  bottom,  and  the  warm  air  flowing  away 
from  the  warm  area  at  the  top.  Over  the  warm  area  the 
air  moves  upward,  while  over  the  cold  area  the  air  moves 


48 


HEAT    TRANSFERENCE 


downward.      These   movements    are   called    convection    cur- 
rents. 

Convection  currents  take  place  in  liquids  as  well  as  in 
gases,  but  cannot  take  place  in  solids. 

57.  Drafts  in  Chimneys.  —  Drafts  in  chimneys  are  due 
to  convection  currents.     A  fire  is  started  in  the  fire-box  of 

the  furnace.  (Figure  32.)  This  warms 
the  air,  and  causes  it  to  expand  and 
become  lighter  than  the  surrounding  air. 
The  cold  air  then  pushes  the  warm  air 
up  the  chimney  and  takes  its  place  in 
the  fire-box.  This  air  is  then  heated, 
and  the  process  is  repeated,  or  rather  it 
takes  place  continuously.  The  higher 

the  chimney,  the  greater  the  draft. 
FIGURE  32.  — DRAFT 

IN  A  CHIMNEY.  Suppose  the  chimney  (Figure  32)  were  4  ft. 

square  and  100  ft.  high;    and  suppose  the  air 
raised  from  0°  C.  to  273°  C.,  when  the  fire  started. 

4  X  4  X  100  =  1600  cu.  ft.  =  volume  of  the  chimney. 
Now,  air  at  0°  C.  weighs  .08  Ib.  per  cu.  ft. 

1600  X  .08  =  128.00  Ib.  =  wt.  of  air  in  the  chimney,  when  air  is 
cold. 

Since  a  gas  expands  2fj  of  its  volume  at  0°  C.  when  heated  1°  C., 
it  will  double  its  volume  when  heated  to  273°  C. 

Therefore,  since  the  chimney  will  contain  only  1600  cu.  ft.,  £  of  the 
air  must  flow  out. 

|  of  128  Ib.  =  64  Ib.,  wt.  of  air  which  remains  in  the  chimney. 
Now,  since  an  equal  volume  of  air  on  the  outside  weighs  128  Ib., 
ancl   inside  it  weighs  64  Ib.,  the  cold  air  outside  pushes  up  on  the 
warm  air  inside  with  a  force  of  64  Ib.     This  shows  definitely  why  the 
air  rises  in  the  chimney,  or  explains  the  draft. 

58.  Draft  in  a  Kitchen  Range.  —  Figure  33  shows  the 
ordinary  kitchen  range.     The  air  enters  at  the  front  and 


DRAFT  IN   A    KITCHEN   RANGE 

1      Damper 


49 


FIGURE  33.  —  DRAFT  IN  A  KITCHEN  RANGE. 

goes  up  to  the  fire-box.     Here  it  becomes  hot  and,  with  the 
smoke,  passes  up  over  the  oven,  down  at  the  end  and  under 


FIGURE  34.  —  DIAGRAM  OF  A  HOT-AIR  HEATING  SYSTEM. 


50 


HEAT    TRANSFERENCE 


the  hot-water  reservoir,  then  under  the  oven,  and  finally 
up,  at  the  back  of  the  oven,  to  the  stove  pipe.  Thus  we 
see  the  hot  gases  pass  completely  around  the  oven,  except 
in  front,  where  the  door  is  located. 

If  the  oven  is  not  to  be  used,  the  damper  is  closed,  which 
shuts  the  current  off  from  the  oven  and  lets  the  hot  gases 
circulate  only  under  the  top  of  the  stove  and  the  reservoir. 

59.  Hot-air  Heating. 
—  Figure  34  shows  a 
diagram  of  the  modern 
hot-air  heating  system. 
The  furnace  located  in 
the  basement  consists 
of  two  parts,  a  fire- 
box, and  a  sheet-iron 
jacket,  the  two  being 
separated  by  an  air 
space. 

The  air  that  feeds  the 
fire  in  the  fire-box  goes 
in  through  a  hearth,  and 


FIGURE  35.  —  A  HOT-AIR  FURNACE, 


the    smoke     and     gases 
pass  on  up  the  chimney. 

This  air  and  other  gases  never  reach  the  rooms,  nor  are  they 
even  in  contact  with  the  air  that  goes  to  the  rooms.  The 
latter  comes  in  through  the  cold-air  shaft  (from  outside  or 
from  the  basement  itself) ;  is  heated  as  it  passes  between 
the  sheet-iron  jacket  and  the  wall  of  the  fire-box;  then  is 
carried  in  convection  currents  through  pipes  that  lead  to 
the  separate  rooms. 

60.   Hot-water  Tank.  —  Convection  currents   take  place 
in  liquids  as  well  as  in  gases.     Use  is  made  of  this  in  the 


HOT-WATER   HEATING  SYSTEM 


51 


hot-water  tank.     Figure  36  shows  a  hot- water  tank  designed 
to  be  heated  by  a  separate  heater,  or  by  the  furnace  itself. 

The  water  comes  into  the  storage  tank  (.4)  through 
pipe  (/).  A  pipe  (g)  comes  out  of  the  storage  tank  at  the 
bottom  and  passes  up  through  a  pipe  (i),  around  which  is 
the  heater  (B).  This  pipe  then  returns  to  the  top  of  the 
tank  through  (h).  The  pipe  (c)  is  for  drawing  off  the  hot 
water  to  the  places 
where  it  is  needed. 

A  fire  is  started  in 
the  heater  (J5),  causing 
the  water  in  pipe  (i)  to 
expand.  Convection 
currents  are  then  set 
up,  and  the  warm 
water  flows  over  into 
the  top  of  the  tank, 
cold  water  coming  in 
all  the  time  at  pipe  (g).  If  the  furnace  (C)  is  going,  the 
heater  (B)  is  not  needed,  as  the  convection  currents  are 
set  up  through  the  coils  in  the  furnace.  When  water  is 
drawn  off  through  (c),  more  water  is  supplied  through  the 
inlet,  from  the  water  main. 

If  the  water  is  allowed  to  get  too  hot,  steam  is  generated, 
which  may  force  the  water  back  into  the  main,  thus  en- 
dangering the  water  meter. 

61.  Hot- water  Heating  System.  —  Figure  38  shows  a 
modem  hot- water  heating  system.  The  furnace  is  located 
in  the  basement,  and  has  a  boiler  above  the  fire-box.  From 
the  top  of  the  boiler,  pipes  are  led  off  to  the  radiators  in  the 
different  rooms.  Returning  from  the  other  end  of  the 
radiators  are  pipes  to  bring  the  water  back  to  the  bottom 


FIGURE  36. —  DIAGRAM  OF  THE  HEATING 
SYSTEM  OF  A  HOT-WATER  TANK. 


52 


HEAT    TRANSFERENCE 


of  the  boiler.  The  pipes  going  up  to  the  radiators  are 
called  "  risers,"  while  those  coming  down  are  called  "  return 
pipes."  Connected  in  the  system  is  a  pipe  which  goes  up 
to  the  expansion  tank,  usually  placed  in  the  attic. 


FIGURE  37. —  A  KEROSENE  HEATER  USED  IN  CONNECTION  WITH  THE 
HOT-WATER  TANK. 


HOT-WATER  HEATING  SYSTEM 


53 


Before  the  furnace  is  started,  water  is  let  in  from  the  city 
main  until  the  whole  system  is  full  and  water  rises  into  the 
expansion  tank.  Then  the  stop-cock  is  closed,  so  that  no 
more  water  can  get  in  or  out.  When  the  fire  is  started, 


FIGURE  38.  —  DIAGRAM  OF  A  HOT-WATER  HEATING  SYSTEM. 

convection  currents  are  set  up  through  the  pipes,  causing 
hot  water  to  flow  through  the  radiators. 

The  expansion  tank  is  to  protect  the  pipes  from  bursting. 
If  there  were  no  place  for  the  water  to  go  when  the  fire  is 
started,  the  expansion  would  burst  the  boiler  or  the  pipes. 
This  sometimes  happens  if  the  pipe  to  the  expansion  tank 
in  the  attic  freezes. 


54 


HEAT   TRANSFERENCE 


FIGURE  39.  —  A  HOT-WATER  HEATING  SYSTEM  INSTALLED. 


62.  Ventilation.  —  Ventilation  is  the  supplying  of  pure 
air  and  the  removing  of  impure  air  from  rooms  and 
buildings. 


VENTILATION 


55 


It  is  estimated  that  every  person  should  have  3000  cubic 
feet  of  pure  air  per  hour.  There  are  two  distinct  types  of 
ventilation  —  the  natural  systems  and  the  forced  systems. 

In  the  natural  systems  convection  currents  are  depended 
upon  to  change  the  air.  In  many  dwelling  houses  no  special 
means  are  used  for  ventilation ;  open  windows,  doors,  or 
crevices  are  depended  upon  entirely  to  supply  pure  air. 

If  a  window  is  opened  both 
at  the  top  and  bottom,  as  is 
shown  by  Figure  40,  and  a 
lighted  candle  is  held,  first 
at  the  bottom,  and  then  at 
the  top,  of  the  window,  the 
candle  flame  will  blow  to- 
wards the  room  in  the  former 
position,  but  will  blow  out- 
wards when  held  at  the  top, 
showing  that  air  enters  at  the 
bottom  and  leaves  at  the  top. 
This  is  explained  by  convec- 
tion currents.  Opening  win- 
dows is  a  quick  means  of 


Outside 


Inside 


but    it 


FIGURE  40. — -VENTILATION  BY  MEANS 
OF  THE  OPEN  WINDOW. 


getting    ventilation, 
produces  drafts. 

Even  when  the  windows  or  doors  are  dosed,  air  comes 
in  around  the  frames,  where  there  is  not  a  perfect  fit.  This 
supplies  pure  air  and  is  sufficient  in  many  cases  where  very 
few  people  use  the  rooms.  Wind  coming  from  one  side  of 
the  house  often  helps  ventilate  it,  blowing  pure  air  in  on 
one  side  and  forcing  impure  air  out  on  the  other. 

A  grate  or  fireplace  is  a  good  ventilator.     Why? 

One  of  the  simplest  methods  for  special  ventilation  is 


56 


HEAT    TRANSFERENCE 


shown  in  Figure  41.  A  cold  air  vent  is  made  just  below  the 
radiator.  As  the  cold  air  comes  in,  it  is  heated  by  the  radia- 
tor and  made  to  flow  to  all  parts  of  the  room  by  means  of 
convection  currents.  The  impure  air 
leaves  by  way  of  crevices. 

Another  of  the  natural  systems  is 
shown  in  Figure  42.  Here  the  air 
comes  in  from  the  outside,  passes 
around  a  special  heating  device  in  the 
floor,  and  then  is  distributed  by  con- 
vection currents. 
Forced  ventilation  is  used  in  large 


If 


Air  DucT  to  OuTside 


\ 


Air-duct  to  Outside 


FIGURE  41.—  ANOTHER 
METHOD  OF  VENTILA- 
TION. 

is   used    in 

buildings,  such  as  schools,  apartment  houses,  department 
stores,  and  theaters.  In  such  buildings  there  are  great 
numbers  of  people,  and  the  ordinary  method  of  ventilation 
is  not  sufficient  to  supply  the  required  3000  cubic  feet,  per 
hour,  for  each  person. 

Forced- ventilation 
systems  use  fans  to 
make  the  air  move. 
One  way  is  to  draw  the 
impure  air  out  by  means 
of  fans,  allowing  the 
pure  air  to  flow  in  to 
take  its  place.  Other 
methods  force  the  pure 
air  in,  driving  the  im- 
pure air  out. 

Figure  43  shows  a 
forced-ventilating  system  in  which  the  air  is  washed  before 
it  passes  through  the  rooms.  Pure  air,  forced  in  by  the  fan, 
enters  the  washing  room.  The  washing  room  consists  of  a 


Coils  in  Floor 


Heating  Pipe 


FIGURE  42. — VENTILATION  WITH  HEATING 
DEVICE  IN  THE  FLOOR. 


RADIATION 


57 


Heating  Room 


closed  space  in  which  water  is  kept  spraying.  Here  the  air 
has  most  of  the  dust  and  impurities  removed.  Then  it  is 
forced  up  the  pipes  to  the  heating  space,  and  from  there 
it  goes  to  the  places  where  it  is  needed. 

63.  Radiation.  —  Conduction  and  convection,  the  two 
methods  of  transference  of  heat  which  we  have  just  studied, 
are  easily  understood;  but  the  third  method,  radiation,  is 
much  more  difficult  to 
explain.  We  know  that 
heat  travels  from  the 
sun  to  the  earth,  and 
that  it  comes  through 
space  in  the  form  of 
waves  in  the  ether. 

No  one  knows  just 
what  the  ether  is,  but 
there  are  many  facts 
which  prove  its  exist- 
ence. Whatever  it  is, 
it  has  no  weight  or 
body,  but  it  fills  the 
whole  universe. 

Heat  in  the  form  of 
waves  in   the  ether  is 
insensible,   for   sensible    heat   is 
molecules. 

When  heat  waves  strike  opaque  objects,  they  are  partly 
changed  to  sensible  heat  and  partly  reflected  back  as  waves. 
When  they  strike  transparent  objects,  such  as  air,  glass,  clear 
water,  etc.,  they  pass  through  without  heating  the  object. 

Radiation  is  the  transference  of  heat  by  means  of  waves  in 
the  ether. 


Washing  Room 


FIGURE  43.  —  DIAGRAM  OF  A  FORCED- 
VENTILATING  SYSTEM. 


due    to    the    vibration   of 


58  HEAT   TRANSFERENCE 

64.  Radiators.  —  We  must  not  get  the  idea  that  the  sun 
is  the  only  thing  that  sends  out  these  heat  waves,  for  all 
hot  bodies  do  this,  more  or  less.     Any  body  that  sends  out 
heat  waves  is  called  a  radiator. 

All  bodies  at  the  same  temperature  do  not  radiate  their 
heat  at  the  same  rate.  It  is  found  that  rough,  black  bodies 
are  the  best  radiators,  while  smooth,  white,  or  shiny  objects 
radiate  heat  very  slowly. 

65.  Absorbers.  —  Heat   waves    striking   opaque    objects 
are  changed  to  sensible  heat.     These  objects  are  said  to 
absorb  the  heat  waves.     Bodies  which  are  good  radiators, 
namely,    rough   black   ones,    are   also   good   absorbers.     A 
rough,  black  piece  of  iron  will  cool  off  quickly  after  it  is 
heated,  because  it  is  a  good  radiator;    and,  on  the  other 
hand,  it  will  become  warm  quickly  if  placed  where  heat 
waves  fall  on  it,  because  it  is  a  good  absorber. 

66.  Reflectors.  —  Why   are   rough,    black   objects   good 
radiators  and  good  absorbers,  while  smooth,  white,  or  shiny 
objects  are  poor  ones?     The  answer  is  that  smooth,  white, 
or  shiny  objects  are  good  reflectors.     The  heat  waves  fall  on 
them  and  are  reflected  back,  just  as  light  is  reflected  by  a 
mirror.     On  the  other  hand,  when  the  heat  waves  start  to 
leave  the  objects,  the  shiny  surface  turns  them  back  again. 

67.  Applications.  —  In    the   thermos   bottle    (§   53)    the 
glass  and  the  vacuum  stop  conduction  and  convection,  but 
cannot  stop  the  heat  from  radiating  into  or  out  of  the  bottle. 
This  is  stopped  by  the  silver  surfaces.     As  they  are  smooth, 
and  shiny,  any  heat  trying  to  radiate  into  the  bottle  is  re- 
flected  out  again;    and  any  heat  trying  to  radiate  out  is 
reflected   in   again.     Therefore   all   three   avenues   for   the 
transference  of  heat  are  stopped,  so  that  either  hot  or  cold 
liquids  put  into  the  bottle  remain  hot  or  cold. 


APPLICATIONS  59 

A  black,  rough  stove  would  be  more  serviceable  than  a 
bright,  shiny  one.  Why?  What  kind  of  clothes  would 
you  wear  in  hot  weather  or  in  a  warm  climate?  In  a  cold 
climate?  Why? 

Greenhouses  trap  the  heat  of  the  sun  and  do  not  let  it 
out.  The  heat  waves  pass  through  the  glass  of  the  green- 
house and  strike  the  plants  and  soil  and  other  objects, 
which  absorb  the  waves.  In  other  words,  the  waves  are 
changed  to  sensible  heat.  The  glass  walls  are  poor  con- 
ductors ;  so  the  sensible  heat  cannot  get  out. 

Dirty  snow  does  not  melt  evenly,  but  in  holes  and  patches. 
Soot  and  dirt,  being  black,  absorb  the  sun's  rays  and  thus 
melt  the  snow  under  them,  causing  holes  in  the  snow.  Where 
there  is  no  dirt,  the  snow  reflects  the  rays  and  therefore 
melts  more  slowly. 

On  a  sunny  day,  would  the  snow  melt  faster  under  a 
black  woolen  blanket,  or  without  the  blanket?  Would  it 
be  the  same  by  night,  or  if  the  day  were  cloudy  ? 


CHAPTER  IV 
SOURCES  OF  HEAT 

68.  Fuels.  —  We  have  studied  the  nature  of  heat,  have 
seen  what  it  will  do,  and  how  it  is  transferred  from  one 
place  to  another.  Now  comes  the  question,  where  do  we 
get  heat? 

The  sun  is  the  great  source  of  heat,  but  the  sun's  heat 
is  so  widely  distributed  and  so  little  under  our  control,  that 
it  serves  mostly  the  processes  of  nature,  and  for  specific 
purposes  of  service  we  rely  mainly  on  fuels. 

Fuels  are  materials  which  will  supply  heat  when  burned. 
Sixty  years  ago  the  most  common  fuel  was  wood.  What 
fuel  do  you  use  at  home  to  keep  warm  and  to  do  your  cook- 
ing? Most  of  you  will  say  gas,  or  coal. 

There  are  two  distinct  kinds  of  gas  —  natural  gas  and 
artificial  gas.  The  natural  gas  is  forced  directly  from  the 
gas  well  to  your  home.  The  artificial  gas  does  not  come 
from  wells  at  all,  but  is  made  by  baking  soft  coal  and  treat- 
ing it  in  certain  ways. 

Natural  gas  is  much  better  for  heating  purposes  than 
artificial  gas,  since  the  natural  gives  1200  B.  T.  U.'s  per  cubic 
foot,  while  artificial  gas  gives  only  half  as  much,  or  600 
B.  T.  U.'s  per  cubic  foot. 

There  are  many  kinds  of  coal,  but  we  usually  speak  of 
two,  hard  and  soft.  The  hard  coal  is  "  clean,"  that  is,  it 
has  little  dust  in  it  and  gives  off  little  smoke  when  it  burns. 

60 


FUELS 


61 


The  soft  coal  is  full  of  dust  and  its  smoke  is  dense  and 
sooty. 

Hard  coal  yields  about  14,000  B.  T.  U.'s  per  pound,  when 
burned;  while  soft  coal  yields  about  12,000  B.  T.  U.'s  per 
pound.  It  is  never  possible  to  get  all  the  heat  when  a  fuel 


FIGURE  44. —  KEROSENE  USED  AS  A  FUEL  IN  THE  COOK  STOVE. 

is  burned,  but  more  is  available  in  some  fuels  than  in  others. 
This  is  true  of  coal.  Hard  coal  would  give  only  about  2000 
B.  T.  U.'s  per  pound  more  than  soft  coal,  if  one  could  get  all 
the  heat.  But  a  great  deal  more  heat  is  lost  in  the  case  of 
soft  coal  than  in  the  case  of  hard  coal ;  so  that,  in  the  end, 
hard  coal  heats  much  better  than  soft  coal. 

The  following  table  gives  a  few  of  the  materials  used 


62 


SOURCES   OF   HEAT 


for  fuels,  and  the  name  or  kind  of  each.     Opposite  each  kind 
of  fuel  is  the  heat  value. 

Sources  of  Heat 


MATERIAL 

KIND 

HEAT  VALUE 

Coal 

[Hard 

14000  B.T.U.'s  per  Ib. 

Wood     

{  Soft 
[Coke 
/Hard 

12000  B.T.U.'s  per  Ib. 
14000  B.T.U.'s  per  Ib. 
8400  B  T  U  's  per  Ib 

Gas 

\Soft 
{  Natural 

8600  B.T.U.'s  per  Ib. 
1200  B.T.U.'s  per  cu.  ft. 

Oils    ...... 

[  Artificial 
[  Kerosene 
{  Naphtha 

600  B.T.U.'s  per  cu.  ft. 
20000  B.T.U.'s  per  Ib. 
90000  B  T  U  's  per  Ib 

Electricity  .... 

[  Crude  Oil 

18000  B.T.U.'s  per  Ib. 
3411.72  B.  T.  U.'s  per  Kw.  hr. 

(Electricity  is  given  in  this  table,  though  it  is  not  a  fuel.) 

69.  The  Gas  Meter.  —  The  gas  that  you  use  is  measured 
by  a  gas  meter.  The  gas,  flowing  through  the  meter,  moves 
little  fans,  making  the  hands  move  around  on  the  dials. 

1,000,000  100,000  10,000  1,000 


2634 

FIGURE  45.  —  DIALS  OF  A  GAS  METER  SHOWING  A  READING  OF 
263,400  Cu.  FT. 

These  dials  indicate  how  much  gas  has  passed  through  the 
meter.  The  figures  above  the  dials  indicate  the  number  of 
cubic  feet  that  have  passed  when  the  hand  makes  one  com- 
plete revolution. 


HEAT  FROM  FOODS  63 

Figure  45  shows  a  four-dial  meter  with  a  reading  of  263,400 
cu.  ft. 

Always  begin  to  read  from  the  right-hand  side. 

Your  gas  bill  is  made  out  from  these  meter  readings. 
The  meter  man  comes  round  every  month  and  reads  the 
meter.  The  last  month's  reading  is  subtracted  from  the 
present  month's  reading,  and  the  number  of  thousand  (M) 
cubic  feet  of  gas  used  during  the  present  month  is  thus  deter- 
mined. Only  integral  numbers  of  thousand  cubic  feet  are 
counted.  Thus,  if  the  meter  reads  263,400  cu.  ft.,  the  400 
is  not  counted,  but  the  reading  is  called  263  M. 

The  cost  of  natural  gas  in  Cleveland  at  present  is  30^ 
per  M.  while  that  of  artificial  gas  is  80^  per  M. 

Problems 

1.  How  much  hard  coal  is  necessary  to  melt  150  Ib.  of  ice  when 
12  per  cent  of  the  heat  is  available? 

2.  How  much  soft  coal  is  necessary  to  heat  150  Ib.  of  water  from 
40°  F.  to  100°  F.,  only  6  per  cent  of  the  heat  being  available? 

3.  What  will  be  the  cost  of  the  natural  gas  required  to  boil  10  Ib. 
of  water  away,  if  10  per  cent  of  the  heat  is  available?     Natural  gas 
costs  30^  per  M. 

4.  How  many  B.  T.  U.'s  are  given  off  when  a  ton  of  soft  coal  is 
burned  ? 

5.  What  is  the  cost  of  boiling  away  10  Ib.  of  water,  if  artificial  gas 
is  used  at80?f  per  M? 

6.  Draw  a  4-dial  gas  meter  showing  a  reading  of  267,300  cu.  ft. 

7.  What  is  the  month's  natural  gas  bill  if  the  meter  read  246,300  cu. 
ft/last  month  and  252,600  cu.  ft.  this  month? 

70.  Heat  from  Foods.  —  The  energy  we  use  in  the  body 
comes  from  the  foods  we  eat.  In  other  words,  our  food  is 
fuel.  Part  of  the  food  is  used  for  building  and  repairing 
tissue,  but  certain  kinds  are  for  fuel. 

The  United  States  Government  has  made  charts  of  the 


64  SOURCES   OF   HEAT 

building  value  and  the  heat  value  of  most  of  our  foods.  A 
study  of  these  charts  is  to  be  made  at  this  point. 

An  average  laboring  man  should  have  from  3000  to 
3500  great  calories  of  heat  per  day.  A  person  not  at  manual 
labor  should  have  less  —  it  is  estimated  about  2500  great 
calories. 

From  the  table  in  the  Appendix,  make  up  a  day's  menu 
so  that  the  person  shall  get  about  2500  calories.  Figure  the 
cost  of  each  item  and  make  a  total  for  each  meal.  Calcu- 
late the  cost  for  the  whole  day. 

Review  Problems 

1.  What  is  the  nature  of  heat  ? 

2.  What  is  meant  by  the  terms  hot  and  cold? 

3.  Define  temperature. 

4.  Change  25°  F.,   -  16°  F.,  75°  F.  to  the  corresponding  Centi- 
grade readings. 

5.  Change  10°  C.,  -  8°  C.,  80°  C.  to  the  corresponding  Fahrenheit 
readings. 

6.  Define  freezing  point ;  boiling  point. 

7.  Explain  the  effect  of  pressure  on  the  freezing  point;    on  the 
boiling  point. 

8.  Name  and  explain  two  applications  of  the  effect  of  pressure 
on  the  boiling  point. 

9.  What  are  the  three  heat  units  used  ?     Define  each. 

10.  Discuss  heat  of  fusion. 

11.  Discuss  the  refrigerator  as  an  application  of  heat  of  fusion  of 
water. 

12.  Discuss  heat  of  vaporization. 

13.  Discuss  the  double  boiler  as  an  application  of  heat  of  vaporiza- 
tion of  water. 

14.  Explain  distillation. 

16.   What  is  meant  by  "  iceless  refrigeration  "  ? 
16.   How  many  calories  are  necessary  to  melt  20  kg.  of  ice  without 
changing  its  temperature?     (One  kg.  =  1000  grams.) 


REVIEW  PROBLEMS  65 

17.  How  many  B.  T.  U.'s  are  necessary  to  melt  50  Ib.  of  ice  ?     Where 
does  the  heat  come  from  if  the  ice  is  in  a  refrigerator  ? 

18.  If  the  ice  on  a  lake  one  mile  square  is  \  foot  thick,  how  many 
B.  T.  U.'s  are  necessary  to  melt  it?     (Assume  that  ice  weighs  52  Ib. 
per  cu.  ft.  and  is  at  0°  Centigrade.) 

19.  How  many  B.  T.  U.'s  are  given  off  when  6  Ib.  of  steam  con- 
denses in  the  radiator  ? 

20.  Explain  dew. 

21.  Define  specific  heat. 

22.  Name  and  explain  two  applications  of  specific  heat. 

23.  Explain  expansion. 

24.  How  much  will  a  40  cm.  glass  tube  expand  in  length  when 
heated  20°  C.  ? 

25.  How  much  larger  than  the  rest  of  the  glass  will  the  bottom 
of  a  two-inch  drinking  glass  become  when  the  bottom  is  suddenly 
thrust    into   boiling   water    (212°    F.)?      (Assume   that    the   original 
temperature   was   80°   F.)      What   will    this    expansion    do    to    the 
glass  ? 

26.  Explain  the  thermostat. 

27.  Why  do  water  pipes  burst  when  they  freeze  ? 

28.  What  is  the  volume  coefficient  of  expansion  of  a  gas? 

29.  Explain  the  meaning  of  absolute  zero. 

30.  What  application  has  Charles'  Law  to  the  baking  of  bread  and 
cake? 

31.  Explain  conduction. 

32.  Give  three  applications  of  conduction  as  a  method  of  heat 
transference. 

33.  Explain  convection. 

34.  Why  does  the  smoke  flow  out  of  a  chimney? 

35.  Explain  how  the  water  is  heated  in  the  hot-water  tank. 

36.  How  long  would  the  air  in  a  room  20  ft.  X  18  ft.  X  10  ft.  re- 
main healthful  if  five  persons  were  in  it  ? 

37.  What  are  the  two  types  of  ventilation  ? 

38.  Discuss  radiation. 

39.  Discuss  radiators,  absorbers,  and  reflectors. 

40.  Name  and  explain  three  applications  of  radiation. 

41.  What  is  a  fuel? 

42.  How  much  natural  gas  is  necessary  to  heat  100  Ib.  of  water  for 


66  SOURCES   OF   HEAT 

a  bath,  if  the  water  is  at  38°  F.  at  the  beginning,  and  100°  F.  when 
heated  ?     (Assume  that  8  per  cent  of  the  heat  is  available.) 

43.  How  much  soft  coal  is  necessary  to  melt  50  Ib.  of  ice,  if  only 
6  per  cent  of  the  heat  is  available  ? 

44.  What  is  the  cost  per  gallon  of  distilling  water,  if  natural  gas 
is  used  and  10  per  cent  of  the  heat  is  available  ?     (Assume  that  the 
water  has  to  be  raised  from  38°  F.) 

45.  Why  should  the  food  one  eats  have  a  certain  heat  value  ? 


CHAPTER  V 
WAVE   MOTION 

71.  Examples  of  Wave  Motion.  —  Sound  and  light  are 
the  commonest  examples  of  wave  motion ;  but  the  example 
most  readily  seen  is  the  waves  formed  on  water  when  some- 
thing disturbs  its  surface.  If  a  stone  is  thrown  into  still 
water,  a  splash  occurs  at  the  point  where  the  stone  strikes, 
and  waves  travel  outward  in  all  directions  from  this  point. 
If  a  cork,  or  anything  that  will  float,  is  placed  on  the  water, 
it  is  seen  to  bob  up  and  down ;  but  it  does  not  move  away 
from  its  original  position. 

A  similar  example  is  the  waves  produced  in  a  field  of 
grain  when  the  wind  blows  over  it.     The  individual  heads 
of  grain  merely  rise 
and     fall,    but     the    fX 
wave   travels  across 
the  field. 

If  a  rope  or  rubber  FlGURE  46.-WAVE  IN  A  ROPE. 

hose  is  held  station- 
ary at  one  end  and  the  other  end  is  shaken,  waves  will  be 
sent  down  the  rope.  (Figure  46.)  The  waves  travel  from 
one  end  of  the  rope  to  the  other,  but  each  particle  of  the 
rope,  such  as  P,  jumps  up  and  down,  but  does  not  move 
forward. 

Figure  47  shows  a  spiral  spring,  attached  to  a  support 
at  the  top,  having  its  bottom  suddenly  jerked  downward. 

67 


68 


WAVE   MOTION 


FIGURE  47.  —  WAVE 
IN  A  SPRING. 


A  portion  of  the  spring  a  is  stretched,  but  the  rest  of  the  coil 
b  remains  the  same  as  before  it  was  jerked.  The  next  in- 
stant part  a  pulls  down  on  part  b  and 
stretches  b,  letting  a  go  back  to  its  first 
position. 

This  is  a  form  of  wave  in  which  the 
waves  move  along  the  spring,  and  each 
particle  of  the  spring  jerks  backward 
and  forward,  parallel  with  the  spring. 
Waves  can  be  sent  along  rubber  bands 
just  as  along  the  spring  mentioned  above. 
Suppose  a  rubber  ball  is  in  the  center 
of  the  room,  fastened  by  rubber  bands 
to  all  the  walls,  the  ceiling,  and  the  floor. 
(Figure  48.)  Then  suppose  the  rubber 
ball  contracts  suddenly.  All  the  rubber  bands  next  the  ball 
will  be  stretched,  as  shown  in  Figure  49.  Each  stretched 
portion  will,  in  turn,  stretch  the  next  portion ;  and  so  on, 
until  the  effect  runs  out  to  the  ends  of  all  the  rubber  bands, 
just  as  it  did  in  the  spring. 
Since  this  effect  travels  out 
at  the  same  speed  in  all  the 
bands,  we  can  think  of  it  as 
being  a  wave  like  the  wave 
on  the  water. 

72.  Origin  of  Waves.— 
It  is  seen  from  all  the  pre- 
ceding examples  that  waves 
have  to  be  started.  This  is 
always  true.  In  the  case  of 

the    water    wave,    the    Stone     FIGURE  48. -A    RUBBER   BALL    AT- 

'  TACHED    TO    THE    SlDES    OF    A    ROOM 

Started   the   disturbance;     in         BY  MEANS  OF  RUBBER  BANDS. 


CHARACTERISTICS   OF   TRANSVERSE   WAVES      69 

the  field  of  grain,  it  was  the  wind ;  in  the  rope,  your  hand 
was  the  cause.     The  same  thing  was  true  with  the  spring ; 
and    the   contraction   of    the 
rubber  ball  started  the  wave    I 
in  the  rubber  bands. 

73.  Transverse  and  Longi-    FIGURE  49. —  A  stretched  PORTION 

.-,,  OF    A    RUBBER    BAND    NEXT    THE 

tudinal  Waves.  —  There  are       BALL> 
two    motions    in    each    case 

mentioned :  the  motion  of  the  wave,  and  the  motion  of  the 
particles  of  water,  rope,  spring,  rubber,  or  grain  heads. 

The    relative    direc- 

IE. >TF   tions  of  these  two  mo- 
tions    determine     the 

FIGURE  50.  —  SHOWING  DIRECTIONS  OF         t»    j        *  j 

MOTIONS  IN  A  TRANSVERSE  WAVE.  kmd     of     wave     under 

consideration.       Waves 

in  which  the  particles  move  at  right  angles  to  the  direction  in 
which  the  wave  moves  are  called  transverse  waves.  (Figure 
50.)  The  long  arrow  W  indicates  the  direction  of  the  wave, 
and  the  arrow  P  indicates  the  direction  in  which  the  par- 
ticle moves. 

Waves  in  which  the  particles  move  parallel  with  the  direction 
in  which  the  wave  moves  are  called  longitudinal  waves. 
(Figure  51.)  Here  the  p 

two  arrows  are  parallel,    ^^ >w 

and    SO    show    a    longi-         FIGURE  St.- SHOWING  DIRECTIONS  OF 

MOTIONS  IN  A  LONGITUDINAL  WAVE. 

tudinal  wave. 

74.  Characteristics  of  Transverse  Waves. '- —  In  case  of 
the  waves  in  the  water,  in  the  grain,  and  in  the  rope,  we 
find  that,  as  the  waves  follow  one  another,  parts  of  the 
material  are  high  and  other  parts  low.     The  high  parts  a 
and  c  (Figure  52)  are  called  crests,  while   the   low  parts  b 
and  d  are  called  troughs. 


70  WAVE   MOTION 

The  distance  ac  from  one  crest  to  a  corresponding  point 
in  the  next  crest  is  called  a  wave  length;  or  it  may  be  from  one 
trough  to  the  corresponding  point  in  the  next  trough,  bd. 


Wave  Length 


Wave  Length  - 

t  1)  d 

FIGURE  52.  —  CHARACTERISTICS  OF  A  TRANSVERSE  WAVE. 

The  distance  that  each  particle  moves  from  the  position 
of  rest  is  called  the  amplitude,  xy. 

When  a  particle  has  moved  from  x  to  y,  to  t,  to  x,  it  is 
said  to  have  made  one  complete  vibration. 

The  time  required  to  make  one  complete  vibration  is 
called  the  period;  and  the  number  of  vibrations  the  particle 
makes  per  second  is  called  the  frequency. 

75.  Characteristics  of  Longitudinal  Waves.  —  In  longi- 
tudinal waves  we  have  very  nearly  the  same  characteristics 
as  in  transverse  waves. 

Instead  of  having  crests  and  troughs,  we  have  conden- 
sations and  rarefactions.  Figure  53  shows  the  particles  as 

}< —  Wave  Length  — >\ 
I 
i  ' 


!  L4LJ 


a  \c  t>  d\ 

[* Wave  Length — *j 

FIGURE  53.  —  CHARACTERISTICS  OF  A  LONGITUDINAL  WAVE. 

they  would  appear  in  a  rubber  band  if  a  wave  were  traveling 
in  it. 
The  parts  a  and  b  where  the  rubber  particles  are  crowded 


HOW  LONGITUDINAL   WAVES   TRAVEL  71 

together,  are  called  condensations.  The  parts  c  and  d 
where  the  particles  are  stretched  apart,  are  called  rarefactions. 

The  wave  length  is  the  distance  from  one  condensation 
to  the  next,  or  from  one  rarefaction  to  the  next. 

Amplitude,  vibration,  period,  and  frequency  mean  the 
same  as  in  transverse  waves. 

76.  How  Transverse  Waves  Travel.  —  Most  transverse 
waves  travel  in  a  substance  which  has  tensile  strength, 
that  is,  a  substance  which  will  resist  a  pull.  The  wave 
moves  from  one  position  to  another  in  this  way : 

Figure  54  shows  a  wave  in  a  rope,  with  some  of  its  parts 
numbered.  As  the  wave  travels  along  the  rope,  the  particles 


t8       9       10     11      12 

FIGURE  54.  —  THE  START  OF  A  TRANSVERSE  WAVE. 

move  up  and  down ;  or,  as  the  particles  move  up  and  down, 
the  wave  travels  along  the  rope.  It  is  the  motion  of  the 
particles  that  produces  the  wave  motion. 

In  the  figure,  #1  has  been  to  the  top  of  the  swing  and 
has  come  back  to  its  present  position.  Since  #2  is  on  the 
same  rope,  it  is  pulled  along  after  $1.  Also,  #3  is  pulled  by 
#2 ;  and  so  on.  Thus  we  see  that  the  different  particles  are 
affected  in  a  series,  one  after  the  other,  and  not  all  at  once. 

To  state  it  as  briefly  as  possible :  the  wave  travels  by  one 
particle  pulling  the  next  one  after  it. 

77.  How  Longitudinal  Waves  Travel.  —  Longitudinal 
waves  may  travel  in  substances  that  have  tensile  strength, 
but  they  do  not  depend  on  the  pulling  effect  to  make  them 
travel.  Instead,  they  depend  on  the  crowding  effect. 


72  WAVE    MOTION 

As  an  example,  take  the  longitudinal  wave  in  a  spring. 
(Figure  55.)  The  particles  of  the  spring  are  all  crowded 
together  at  d  and  e,  and  are  all  spread  out  at  a  and  c. 

Now,  since  there  is  nothing  to  keep  the  spring  stretched 
at  positions  a  and  c,  and  compressed  at  d  and  e,  the  crowded 
portions  d  and  e  will  expand  and  tend  to  compress  the  parts 
a  arid  c. 

If  this  action  should  stop  when  the  spring  is  everywhere 
stretched  alike,  the  wave  would  stop ;  but  it  is  the  same  as 


d  a  e  c 

FIGURE  55. — How  A  LONGITUDINAL  WAVE  TRAVELS. 

when  you  run  fast  and  then  try  to  stop  suddenly.  You  go 
farther  than  you  intended.  The  same  is  true  of  the  parts 
of  the  spring.  The  crowded  portions  expand  too  much, 
causing  an  overstretched  portion;  and  the  part  that  was 
stretched  before  is  compressed.  In  this  way,  the  crowding 
effect  is  passed  along,  and  the  wave  is  said  to  travel. 

78.   Velocity    of    Waves.  —  Waves    travel    at    different 
speeds.     If  the  rope  is  stretched  tight,  the  waves  will  travel 
faster    than    if    the    rope   is    loose. 


~  ~1/-\       l/-v       A    They  would    travel   more  slowly  if 
\y      \s       V/l      the  rope  were  large  and  heavy. 

On  the  other  hand,  the  frequency 
FIGURE  56.- VELOCITY  =       of  the  vibration  does  not  affect  the 
FREQUENCY  x  WAVE  LENGTH. 

speed   of   the   wave,  nor  does   the 

amplitude.     If  the  frequency  is  high,  the  waves  are  short; 
but  if  the  frequency  is  low,  the  waves  are  long. 

During  one  vibration  the  wave  travels  1  wave  length, 
L.  (Figure  56.)  During  two  vibrations  the  wave  travels  2 
wave  lengths,  2  L ;  while  during  three  vibrations  it  travels  3 


VELOCITY  OF   WAVES  73 

wave  lengths,  3  L.  From  this  we  see  that  in  N  vibrations 
the  wave  will  travel  NL. 

Now,  N  is  the  number  that  usually  stands  for  the  fre- 
quency; so  NL  is  the  distance  the  wave  will  travel  in  1 
second. 

The  distance  an  object  travels  in  a  second  is  called  its 
velocity;  so  the  velocity  of  a  wave  is  the  frequency  times  the 
wave  length;  or 

Velocity  =  Frequency  X  Wave  Length 
or  V  =  NL. 


CHAPTER  VI 
SOUND 

79.  Definition  of  Sound.  —  Sound  may  be  defined  as  a 
vibration  of  such  a  frequency  that  it  may  be  detected  by  the  ear. 

There  are  three  things  necessary  for  sound :  (1)  some 
vibrating  object  to  start  the  vibration ;  (2)  some  medium 
to  carry  the  vibration ;  (3)  something  to  receive  the  sound. 

The  vibrating  object  to  start  the  vibration  may  be  a  tun- 
ing fork,  piano  wire,  bell,  drum,  etc. 

The  air  is  the  medium  which  usually  carries  the  waves 
from  the  vibrating  body  to  the  ear  which  receives  it.  Water 
will  do  this  very  well ;  and,  in  fact,  any  material  body  will 
carry  the  vibration.  A  vacuum  will  not.  This  can  be 
shown  by  placing  an  alarm  clock  in  a  jar  and  then  exhausting 
the  air  with  a  pump.  The  clock  will  become  inaudible,  but 
when  the  air  is  let  in  again  it  can  be  heard. 

The  thing  that  usually  receives  the  sound  is  the  ear, 
but  sometimes  the  vibration  is  detected  by  other  things. 

80.  Nature  of  Sound.  —  Sound  waves  travel  through  the 
air,  but  we  cannot  see  the  effect,  since  the  air  is  transparent. 
Suppose  that  the  air  were  made  so  we  could  see  it,  and  that, 
just  as  a  sound  wave  passed  through  it,  an  instantaneous 
photograph  were  made  of  the  air.     How  would  it  look  ? 

Figure  57  shows  the  condition  of  the  air  at  a  certain  in- 
stant when  a  sound  wave  is  passing  through  it.  At  the  point, 
a,  where  the  vibration  started,  the  air  is  compressed.  Around 

74 


VELOCITY  OF  SOUND  75 

this  the  air  is  rare,  6;   still  farther  out,  it  is  compressed,  c; 
and  it  is  again  rare  at  d,  etc. 

If  pressure  gauges  were  placed  around  in  different  parts 
of  the  room  while  the  sound-wave  was  passing,  some  would 
show  high  pressures  while  others  showed  low  pressures. 
This  is  because  the  vibrations  crowd  the  air  together  at  some 
places  and  stretch  it  out  at  others.  These  places  are  in  the 
shape  of  spheres.  The  spheres  are 
alternately  places  of  high  and  low 
pressures. 

We  have  described  the  air  at  an 
instant  while  the  wave  is  traveling 
through  it.  The  next  question  is,  how 
do  the  waves  travel  ? 

Sound   waves   are   longitudinal,   and 

FIGURE  57.  — A  SOUND 
depend  on  the  crowding  enect  lor  their          v/AVE  IN  AIR. 

motion.  For  example,  in  Figure  57,  a,  c, 
etc.,  are  at  high  pressures ;  while  b,  d,  etc.,  are  at  low  pres- 
sures; so  the  air  in  the  high  pressures  will  push  outward, 
crowding  the  air  in  the  low  pressures.  This  causes  the  air 
at  the  .low  pressures  to  become  condensed,  and  form  high 
pressures.  In  this  way  the  high  pressures  travel  outward. 
The  low  pressures  follow  in  alternate  order. 

You  will  notice  that  each  particle  of  air  moves  only  back- 
ward and  forward,  while  the  wave  always  moves  forward. 

81.  Velocity  of  Sound.  —  At  0°  C.  sound  travels  1087 
feet  per  second.  Examples  are  common  which  show  that 
sound  waves  take  time  to  travel.  You  can  always  see  the 
steam  before  you  can  hear  the  whistle.  Often  you  can  see 
a  carpenter  hit  a  nail  and  later  hear  the  sound.  As  in  the 
case  of  all  waves,  V  =NL.  This  formula  is  used  in  find- 
ing the  velocity  of  sound. 


76  SOUND 

82.  Effect  of  Temperature  on  Velocity  of  Sound.  —  You 
will  notice  that  the  temperature  0°  C.  was  mentioned  when 
the  velocity  of  sound  was  given  as  1087  feet  per  second. 
This  is  because  a  rise  or  fall  in  temperature  changes  the 
velocity  of  sound.     A  rise  of  1°  C.  makes  the  velocity  2 
feet  per  second  greater;  and  a  fall  of  1°  C.  makes  the  velocity 
2  feet  per  second  less. 

Thus  at  20°  C.  the  velocity  will  be  1087  +  (2  X  20)  =  1087  +  40 
=  1127  feet  per  second. 

Since  a  rise  in  temperature  causes  air  to  expand,  at  a 
higher  temperature  the  air  is  less  dense,  and  is  thus  more 
easily  moved.  This  explains  the  change  in  velocity  with  a 
change  in  temperature. 

83.  Natural  Free  Period.  —  Any  object  such  as  a  pendu- 
lum, a  tuning  fork,  a  swing,  a  string,  etc.  will  vibrate  with  a 
certain  period  if  allowed  to  swing  freely.     This  period  is 
called  its  natural  free  period. 

84.  Resonance.  —  In   starting  to   swing   some    one,   the 
push  must  always  come  at  a  certain  time.     The  push  must 
be  in  unison  with  the  motion  of  the  swing.     This  is  called 
resonance. 

Bridges  can  be  set  in  motion  if  the  even  step  of  those 
crossing  the  bridge  coincides  with  the  natural  free  period 
of  the  bridge.  For  this  reason,  soldiers  break  step  while 
crossing  bridges. 

One  tuning  fork  will  be  set  in  vibration  by  another,  if 
they  have  the  same  natural  free  period.  This  is  true  of  all 
musical  instruments. 

The  principle  of  resonance  can  be  stated  in  this  manner : 
Any  object  free  to  vibrate  will  be  set  in  motion  by  periodic  dis- 
turbances coming  in  the  natural  free  period  of  the  object. 


HOW    WE   HEAR  77 

85.  The  Ear.  —  The  ear  is  the  instrument  with  which 
we   receive   sound.     The   receiving   is  done  in  accordance 
with  the  principle  of  resonance.     Figure  58  shows  a  section 
of  the  ear.     The  part  (a)  is  that  which  we  can  see  outside  the 
head,  and  is  called  the  external  ear.     From  this  a  tube  leads 
into  the  middle  ear  (b) .     Over  the  end  of  this  tube  is  stretched 
a    membrane    (d)    called    the 

ear-drum.  In  the  middle  ear, 
attached  to  the  ear-drum,  is 
a  series  of  three  little  bones. 
The  last  of  these  fits  up 

against  the  end    of   a    spiral 

.    t          n    i  ji  77  •  FIGURE  58. —  DIAGRAM  OF  THE 

tube  called  the  cochlea  or  inner  EAR 

ear  (c). 

The  cochlea  is  a  bony  tube  making  two  and  one  half  turns 
like  a  snail  shell.  This  tube  is  filled  with  a  liquid;  and 
stretched  from  one  side  to  the  other  are  about  7000  strings, 
all  of  different  lengths,  and  ranging  in  frequency  from  about 
16  to  10,000  vibrations  per  second.  The  tube  (e)  is  the 
eustachian  tube,  which  leads  from  the  middle  ear  down  into 
the  throat. 

86.  How  We  Hear.  —  A  sound  wave  consists  of  a  con- 
densation and  a  rarefaction,  or  a  high  and  a  low  pressure. 
The  external  ear  acts  as  a  funnel  and  directs  the  sound  wave 
into  the  tube  to  the  ear-drum.     When  the  high  pressure 
strikes  the  ear-drum,  the  membrane  is  pushed  inward,  and 
then  when  the  low  pressure  comes  it  is  pushed  outward. 
This    sets    the    three    bones    in    motion,    and    the    small 
stirrup-shaped    bone    hammers    on    the    opening    to    the 
inner  ear.      This  makes  the  liquid  in   the  shell-like  tube 
vibrate  the  same  as  the  air  outside  the  ear.     One  of  the 
7000   strings  —  the   one   that    has    the   same   natural    free 


78  SOUND 

period  —  will  be  set  to  vibrating  by  the  principle  of  reso- 
nance. 

Thus  far  the  process  is  purely  mechanica1,  and  would 
take  place  whether  the  person  were  awake,  asleep,  or  even 
dead. 

To  distinguish  between  different  sounds,  or  even  to  become 
conscious  of  them,  is  a  psychological  process.  Each  of  the 
7000  strings  has  a  nerve  to  the  brain.  Here  it  affects  its 
own  particular  brain  cell,  thus  making  the  person  conscious 
of  a  sound.  After  many  similar  experiences  the  person  is 
able  to  recognize  a  sound  and  distinguish  it  from  other 
sounds. 

If  sounds  of  different  frequencies  come  into  the  ear,  the 
several  corresponding  strings  will  vibrate,  and  the  person 
hears  a  combination  of  sounds. 

87.  Reenforcement,  Interference,  and  Beats.  —  If  two 
sound  waves  travel  out  together  and  are  of  different  fre- 


FIGURE  59.  —  REENFORCEMENT,  INTERFERENCE,  AND  BEATS  ILLUSTRATED. 

quencies,   they   will   reenforce   one   another   at   times,   and 
interfere  with  one  another  at  other  times. 

Figure  59  shows  two  waves  of  different  frequencies  start- 
ing out  together.  At  a  they  are  making  condensations  and 
rarefactions  at  the  same  time,  and  thus  they  increase  the 
effect,  or  reenforce  one  another.  At  b  one  wave  has  vibrated 
faster  than  the  other,  and  is  making  a  rarefaction  while 


PITCH  79 

the  other  is  making  a  condensation.  This  is  an  attempt 
to  make  both  a  high  pressure  and  a  low  pressure  at  the 
same  place  at  the  same  time.  The  result  is  neither.  One 
interferes  with  the  other. 

When  the  two  waves  reenforce  one  another,  a  loud  sound 
is  heard,  and  this  is  called  a  beat.  A  beat  occurs  every  time 
one  vibrating  body  gains  one  vibration  on  the  other. 

If  the  frequencies  of  the  vibrating  bodies  do  not  differ 
by  more  than  ten,  the  ear  is  able  to  distinguish  the  separate 
beats ;  but  if  they  differ  by  more  than  ten,  then  the  beats 
come  so  fast  that  the  ear  hears  the  series  of  beats  as  a  new 
sound,  and  not  as  a  series  of  separate  sounds. 

88.  Characteristics  of  Sound.  —  Sounds  differ  from  one 
another    in    three    different    ways.     These    differences    are 
called  the  characteristics  of  sound,  and  are  named  intensity, 
pitch,  and  quality. 

89.  Intensity.  —  The  intensity  of  sound  means  its  loud- 
ness,  and  depends  upon  the  amplitude  of  the  vibration.     A 
bell  struck  very  hard  with  a  hammer  will  give  off  a  loud 
sound  because  the  sides  of  the  bell  are  made  to  swing  with  a 
large  amplitude.     As  the  amplitude  gets  smaller,  the  sound 
dies  out  and  finally  stops. 

90.  Pitch.  —  The  pitch  depends  upon  the  frequency  of 
the  vibration.     A  string  vibrating  256  times  per  second  has 
a  different  pitch  from  one  vibrating  384  times  per  second, 
even  if  they  are  struck  with  the  same  force.     On  the  other 
hand,  a  string  may  be  struck  gently  or  hard,  and  it  will 
always  give  off  the  same  pitch.     So  the  pitch  is  independent 
of  the  amplitude. 

A  pitch  is  said  to  be  high  or  low,  according  to  the  frequency 
of  vibration.  The  greater  the  frequency,  the  higher  the 
pitch. 


80  SOUND 

91.  Quality.  —  The  quality  of  a  sound  depends  upon  its 
overtones.     The  overtone  is  the  thing  which  makes  it  possible 
to  distinguish  one  person's  voice  from  another's,  or  to  tell 
the  difference  between  a  piano  and  a  violin,  etc. 

92.  Fundamental    and    Overtones.  —  When    an    object, 
such  as  a  violin  string,  is  giving  its  lowest  tone,  it  is  said  to 
be  giving  its  fundamental.     The  string  vibrates  back  and 

forth  as  a  whole,  just  like  a  rope 
that  is  being  swung  for  some  one  to 
jump  it.  We  are  apt  to  think  this 

FIGURE  60.  — VIBRATION  OF  A    is  the  only  way  a  string  will  vibrate, 
STRING   IN    SEGMENTS   AND     fc          h[      {  Th  j 

ALSO  AS  A  WHOLE. 

will  break  up  into  segments  which 

vibrate  and  in  that  way  give  off  a  higher  tone.  These 
higher  tones  are  called  overtones. 

A  string  may  be  giving  several  overtones  and  the  funda- 
mental at  the  same  time.  It  is  the  presence  of  the  over- 
tones that  changes  the  quality  of  the  sound. 

Figure  60  shows  a  string  vibrating  as  a  whole  and  also  in 
segments. 

93.  Analysis  of  Sound  Waves.  —  It  has  been  known  for 
many  years  that  sound  waves  consist  of  fundamentals  and 
overtones,  but  it  is  hard  to  tell  just  what  overtones    are 
present.     In  other  words,  it  is  hard  to  analyze  a  sound  wave 
and  tell  just  what  waves  it  is  made  of. 

During  the  latter  part  of  the  nineteenth  century  a  scientist 
named  Helmholtz  succeeded  in  analyzing  sound  waves. 
He  made  hundreds  of  resonators  (Figure  61),  all  of 
different  sizes,  ranging  from  about  a  half-inch  in  diameter 
to  several  feet  in  diameter.  By  testing  a  certain  sound 
with  each  of  these  hundreds  of  resonators  he  was  able  to 
determine  which  ones  were  in  tune  with  that  sound.  The 


LAWS   OF   VIBRATING  STRINGS  81 

ones  that  had   the  same  free  period  vibrated;    the  others 
did  not. 

The  most  recent  and  most  successful  attempt  to  analyze 
sound  waves  was  made  by  Dr.  Dayton  Miller  of  Case 
School  of  Applied  Science,  who  is  still  working  on  the  prob- 
lem. He  has  made  a  machine  which  will  transform  the 
sound  waves  into  a  vibrating  ray  of  light,  so  that  the  wave 
can  be  thrown  upon  a  screen  and  seen  with  the  eye.  He  also 
throws  this  ray  on  a  photographic  plate  and  takes  a  picture 
of  the  wave,  making  it  possible  to  study  the  wave  at  leisure. 


a  be 

FIGURE  61.  —  HELMHOLTZ  RESONATORS. 

Dr.  Miller  is  now  perfecting  another  machine,  which  will 
analyze  the  wave  after  it  has  been  taken  on  a  photographic 
plate.  When  this  is  successfully  accomplished,  he  will 
be  able  to  take  any  sound  wave  and  tell  how  many  and  what 
overtones  are  present. 

With  Dr.  Miller's  machine  the  differences  between  singing 
voices  are  easily  seen.  Some  singers  have  many  harmonious 
overtones,  while  others  have  very  few. 

Figures  62,  63,  64,  and  65  show  samples  of  waves  given 
by  different  singers. 

94.  Laws  of  Vibrating  Strings.  —  The  pitch  of  a  string 
may  be  changed  in  three  ways:  by  changing  (1)  its  length, 
or  (2)  its  tension,  or  (3)  its  diameter.  The  tighter  it  is,  the 


FIGURE  62. —  PHOTOGRAPH  OF  SOUND  WAVE  PRODUCED  BY  SPEAKING 
THE  VOWEL  "A"  AS  IN  "FATHER." 


FIGURE  63.  —  PHOTOGRAPH  OF  SOUND  WAVE  PRODUCED  BY  THE  SOPRANO 
SINGING  ALONE  IN  THE  SEXTET  FROM  "  LUCIA." 


u; 


FIGURE  64.  —  PHOTOGRAPH  OF  SOUND  WAVE  PRODUCED  BY  THE  SOPRANO 
AND  BARITONE  SINGING  TOGETHER  IN  THE  SEXTET  FROM  "  LUCIA." 


RESONANCE  IN  CLOSED  PIPES        83 


FIGURE  65. —  PHOTOGRAPH  OF  SOUND  WAVE  PRODUCED  BY  ALL  Six 
SINGING  TOGETHER  IN  THE  SEXTET  FROM  "  LUCIA." 

faster  it  vibrates ;    the  longer  it  is  or  the  thicker  it  is,  the 
slower  are  its  vibrations. 

The   laws   concerning  these   three   things   are   stated   as 
follows : 

(1)  The  diameter  and  tension  remaining  the  same,  the 
frequency  of  a  string  varies  inversely  as  its  length. 

(2)  The  length  and  tension  remaining  the  same,  the  fre- 
quency of  a  string  varies  inversely  as  the  diameter. 

(3)  The  length  and  diameter  remaining  the  same,  the 
frequency  of  a  string  varies  directly  as  the  square  root  of  the 
tension. 

95.  Resonance  in  Closed  Pipes.  —  If  a  tuning  fork  is 
struck  and  then  held  over  a  pipe  closed  at  the  bottom,  the 
pipe  will  reenforce  the  sound  of  the 
fork,  provided  that  the  tube  is  of  the  \ 
proper  length. 

When  the  fork  moves  from  a  to  6 
(Figure  66),  a  condensation  is  made 
in  front  of  the  fork  and  travels  down 
the  tube  to  the  bottom  and  back  to 
the  mouth  again,  while  the  fork  moves  J~E  66.  _  RESONANCE 
down  to  6.  At  this  instant  the  fork  IN  A  CLOSED  PIPE. 


84  SOUND 

starts  back  toward  a,  forming  another  condensation  in 
front  of  the  fork ;  but  since  a  condensation  is  already  com- 
ing out  of  the  tube  at  this  instant,  this  forms  a  double  con- 
densation, making  a  loud  sound. 

In  the  same  way  the  rarefactions  are  reenforced.  This 
action  will  take  place  only  when  the  tube  is  of  the  proper 
length.  The  reflected  condensation  must  be  just  coming 
out  of  the  tube  when  the  fork  is  ready  to  flip  back  from  b  to 
a ;  and  the  reflected  rarefaction  must  be  coming  out  when 
the  fork  is  ready  to  flip  back  from  a  to  b. 

Now,  since  a  condensation  travels  down  and  back,  or 
twice  the  length  of  the  tube,  while  the  fork  goes  from  a  to 
6,  or  one  half  vibration,  the  sound  will  travel  four  times  the 
length  of  the  tube  during  a  whole  vibration.  Therefore  the 
closed  pipe  is  one  fourth  wave  length. 

By  this  method  the  velocity  of  sound  may  be  determined. 
The  wave  length  is  found  by  multiplying  the  length  of  the 
tube  by  four.     The  frequency  is  al- 
ways marked  on  the  fork.     Then,  by 
formula : 

V  =  NL. 

96.  Resonance  in   Open   Pipes.  — 

If  the  pipe  is  open  instead  of  closed 
at  the  bottom  (Figure  67),  the  con- 
densation will  travel  down  to  the  end, 
FIGURE  67  -  RESONANCE        d       m   ^  t  rarefaction  in- 

IN  AN  OPEN  PIPE.  t  J 

stead  of  a  condensation;   so  the  fork 

must  be  back  at  a  again  before  this  rarefaction  gets  to  the 
top.  That  is,  while  the  sound  travels  down  and  back,  the 
fork  must  make  a  complete  vibration.  Therefore  the  pipe 
is  one  half  wave  length. 


CHAPTER  VII 
BASIS   FOR   MUSIC 

97.  Music  and  Noise.  —  The  prime  difference  between 
music  and  noise  is  that  in  music  the  sounds  have  rhythm 
while  in  noise  they  do  not.     By  rhythm  is  meant  that  the 
sounds  come  at  regular  periodic  intervals. 

The  music  of  the  savages  consists  almost  entirely  of  beating 
time,  while  the  music  of  civilized  people  goes  farther  than 
this,  and  consists  of  rhythm  and  harmony. 

98.  Harmony.  —  Two  or  more  tones  are  said  to  be  in 
harmony  if  their  combination  is  pleasant  to  hear.     Har- 
mony, then,  is  the  combining  of  musical  tones,  according  to 
given  laws,  so  that  they  will  be  pleasing  to  the  ear. 

One  of  the  laws  of  harmony  is,  the  ratios  of  two  tones  must 
be  in  a  simple  ratio  if  they  are  to  be  in  harmony.  By  "  simple 
ratios  "  is  meant,  such  ratios  as  {,  f-,  f,  |,,f,  f,  f,  f,  etc. 

The  reason  why  tones  having  their  frequencies  in  simple 
ratios  are  harmonious  is  a  matter  of  supposition.  It  is 
supposed  that  the  mind  likes  system,  and,  more  than  that, 
simplicity  of  system.  The  most  simple  method  in  which 
soldiers  can  march  is  in  step;  the  next  simplest  is  every 
other  soldier  making  two  steps  to  his  neighbor's  one;  the 
next  is  three  steps  to  two;  and  so  on.  As  soon  as  the  ratio 
gets  into  large  numbers,  the  mind  fails  to  grasp  the  system, 
and  the  marching  soldiers  become  a  mob. 

The  same  is  true  of  sound.  When  the  ratios  are  simple, 

85 


86  BASIS   FOR   MUSIC 

the  mind  grasps  the  relation  and  is  pleased ;  but  when  the 
ratios  become  complex,  the  mind  fails  to  detect  any  relation 
whatever,  and  a  discord  results. 

99.  Major  Triads.  —  When  the  frequencies  of  three  tones 
are  in  the  ratio  4:5:6,  those  three  tones  are  called  a  triad. 
In  music  there  are  three  triads,  called  major  triads.     They 

are : 

1.  Tonic  -C,E,G 

2.  Dominant  —  G,  B,  dz 

3.  Subdominant  —  F,  A,  c2 

100.  Major   Scale.  —  The   eight   notes  which   form   the 
major  triads,  when  arranged  in  the  proper  order,  form  what 
is  called  the  major  scale. 

CDEFGABc2 

The  frequency  of  each  of  the  tones  in  the  major  scale 
can  be  found  by  the  ratios  of  the  major  triads. 

C:E:G} 

G:  B\(k  \   =4:5:6 

The  frequency  of  C  can  be  taken  as  any  number,  and  then 
the  frequencies  of  each  of  the  others  can  be  determined  from 
it. 

If      C  =  256  C  =  256 

E  _  5  G  _  fi 

C  ~  4  C  =  4 

F-*    r  n      5    r 

*4'  -4' 

r  /> 

E  =  '-  •  256  =  320  G  =  -  -  256  =  384 

By  this  method  the  frequencies  of  all  notes  can  be  found. 
Construct  the  major  scale  and  calculate  all  the  frequencies. 


THE   CHROMATIC  SCALE  87 

101.  The  Musical  Interval.  —  The  ratio  of  the  frequencies 
of  any  two  tones  is  called  the  musical  interval  between  those 
tones. 

The  musical  intervals  between  consecutive  tones  in  the 
octave,  and  the  intervals  between  each  tone  and  C  are  given 
as  follows  : 

Letter    ......        C       D       E        F        G        A        B       c2 

Frequency      ....     256     288     320     341|     384     426|    480     512 

Interval   between  con- 

secutive tones      .     .  f       -V°-        if       I        V         I         If 

Interval  between  each 

tone  and  C     ...       1         f        J         |         f          f        -1-/       2 

There  are  a  few  musical  intervals  of  more  importance 
than  others,  and  these  are  given  special  names.  Thus  -J-  = 
unison;  f  =  a  fifth;  J  =  a  fourth;  f  =  a  major  third;  ff  = 
a  half  step;  and  f  =  an  octave. 

102.  The  Chromatic  Scale.  —  For  certain  purposes  it  is 
often  advisable  to  start  triads  on  other  notes  than  C,  G,  and 
F.     This  requires  other  notes  than  those  in  the  major  scale. 
By  starting  triads  on  each  of  the  other  notes  of  the  major 
scale  we  have  : 


E  :  Xv  :  X2 
A    Xi  :  X, 


Figuring  out  the  frequencies  of  these  unknown  notes,  we 
find  they  are  in  the  first  triad  : 

f  =f;   Zt-f   -288  =  360 

A2-?;   X*=-A    •  288=432 
D       4  4 


88  BASIS   FOR   MUSIC 

Now,  360'  falls  between  F  and  0,  and  432  falls  between  A 
and  B;  so  they  are  called  F -sharp  and  A-sharp,  respectively. 
Thus  the  first  triad  is  D,  F-sharp,  and  A-sharp. 

When  all  these  unknown  frequencies  are  calculated,  it 
is  found  that  there  are  five  new  notes  wrhich  fall  in  betwreen 
the  other  notes  of  the  major  scale,  and  a  new  scale  is  built 
up,  using  the  major  scale,  with  the  five  new  notes  added 
in  their  proper  places.  This  new  scale  is  called  the  chromatic 
scale. 

The  notes  in  it  are : 

C,  C-sharp,  D,  D-sharp,  E,  F,  F-sharp,  G,  G-sharp,  A,  A-sharp,  B,  cz. 

103.  Tempered  Scale. —  The  musical  intervals  between 
the  consecutive  notes  in  the  chromatic  scale  are  not  all 
equal.  But  in  the  piano  and  similar  instruments  the  notes 
are  made  at  equal  intervals.  This  new  scale  is  called  the 
tempered  scale.  The  musical  interval  between  consecutive 
notes  is 

%"  =  1.095 

This  musical  interval  is  calculated  by  this  method : 
There  are  twelve  equal  intervals  in  the  tempered  scale. 
Suppose  we  let  a-  equal  the  numerical  value  of  this  interval. 

Then  C-sharp  =  C  •  x 

D  =  C-sharp  •  x  =  C  •  x  •  x 
D-sharp  =  D-x  =  C-x-x-x. 

And  so  on  for  the  complete  scale. 

Thereforec2  =  C  •  x12', 
but  .c2  =  C  -  2. 

Therefore  xn  =  2, 


or  x  =  V2. 


104.    Standard  Pitch.  —  In  order  that  a  piece  of  music 
may  be  played  as  intended,  there  must  be  a  standard  pitch 


MUSICAL  INSTRUMENTS  89 

for  C.  There  are  several  standards,  the  commonest  being 
the  "  International  Standard  Pitch,"  which  makes  C  =  261. 
105.  Musical  Instruments.  —  The  student  is  here  asked 
to  report  on  one  musical  instrument,  covering  the  following 
points : 

1 .  Description  of  the  instrument. 

2.  How  the  sound  is  produced. 

3.  How  the  pitch  is  determined. 

4.  What  the  principal  use  of  the  instrument  is. 


Review  Problems 

1.  Give  five  examples  of  wave  motion. 

2.  Distinguish  between  transverse  and  longitudinal  waves. 

3.  What  are  the  characteristics  of  transverse  waves?     Define  each. 

4.  What  are  the  characteristics  of  longitudinal  waves?     Define 
each. 

5.  Explain  how  transverse  waves  travel. 

6.  Explain  how  longitudinal  waves  travel. 

7.  If  a  rope  be  shaken  at  the  rate  of  3  vibrations  per  second,  and 
the  waves  are  10  feet  long,  how  fast  do  the  waves  travel? 

8.  Explain  the  nature  of  sound. 

9.  If  3  seconds  after  you  see  the  lightning  you  hear  the  thunder, 
how  far  away  was  the  lightning  ?     Take  the  temperature  as  18°  C. 

10.  Why  does  a  vase,  or  any  other  small  article  in  the  room,  often 
rattle  when  the  piano  is  played  ? 

11.  Why  is  it  dangerous  for  the  audience  to  stamp  the  feet  in  a  large 
auditorium  ? 

12.  Describs  the  ear. 

13.  How  do  we  hear? 

14.  Why  do  heavy  explosions,  such  as  the  firing  of  cannon,  often 
cause  deafness? 

15.  What  are  beats  ? 

16.  What  is   the   cause   of   "  dead   points  "  —  places   where   it  is 
difficult  to  hear  —  in  an  auditorium  ? 


90  BASIS   FOR    MUSIC 

17.  Name  the  characteristics   of  sound.     Upon   what  does  each 
depend  ? 

18.  What  is  the  difference  between  a  "sweet"  and  a  "harsh" 
voice  ? 

19.  If  two  strings  are  the  same,  except  that  one  is  40  cm.  long  and 
the  other  is  60  cm.  long,  what  is  the  ratio  of  their  frequencies?     If 
the  40-cm.  string  vibrates  300  times  per  second,  what  is  the  frequency 
of  the  other? 

20.  Why  are  some  of  the  strings  on  a  piano  large  and  others  small  ? 

21.  How  does  a  piano  tuner  tune  a  piano?     Why  does  this  change 
the  pitch  ? 

22.  Why  does  a  pipe  organ  have  many  pipes,  all  of  different  lengths? 

23.  Explain  how  to  find  the  velocity  of  sound. 

24.  What  is  rhythm  ?     Harmony  ? 

25.  What  is  the  leason  why  tones  must  be  in  simple  ratios  to  be  in 
harmony  ? 

26.  Construct  a  major  scale,  using  C  as  96. 

27.  Construct  a  chromatic  scale,  using  E  as  409. 

28.  What  is  the  tempered  scale? 

29.  Why  is  the  common  musical  interval  between  consecutive  notes 
in  the  tempered  scale  1 .059  ? 

30.  Name  two  other  standard  pitches  besides  the  International 
Standard  Pitch.     (Outside  reference.) 

31.  What  is  the  use  of  the  sounding  board  in  a  piano? 

32.  Why  does  a  phonograph  give  a  higher  pitch  when  run  fast? 

33.  What  changes  the  pitch  of  a  slide  trombone  ? 

34.  What  changes  the  pitch  of  a  cornet? 

35.  Why  does  the  piano  have  the  tempered  scale?     Figure  out  the 
frequencies  of  all  notes  on  the  piano,  using  A  as  435. 


CHAPTER  VIII 
> 

LIGHT 

106.  Nature  of  Light.  —  Nobody  knows  the  exact  nature 
of  light.     Many  theories  have  been  offered,  but  none  has 
been  accepted  as  final.     But  we  know  a  great  deal  about 
light,  even  if  we  do  not  know  just  what  it  is.     In  this  dis- 
cussion, we  shall  take  up  facts  already  proved  and  mention 
some  of  the  latest  theories. 

It  is  definitely  known  that  light  is  one  of  the  many  forms  of 
energy,  and  that  it  has  much  in  common  with  radiant  heat. 

107.  Theory    of   Production   of   Light.  —  In    almost   all 
cases,  light  is  produced  by  something  hot.     (Fluorescence 
and  phosphorescence  are  exceptions.)     Our  common  sources 
of  light  are  the  sun,  a  fire,  a  candle,  a  lamp,  or  some  other 
very  hot  body. 

It  is  thought  that  the  rapid  vibration  of  the  molecules  of 
the  heated  body  sets  up  waves  in  the  ether,  and  that  the 
ether  transmits  these  waves  through  space.  These  waves 
are  of  different  lengths,  depending  upon  the  frequency  of 
the  vibration  of  the  molecules.  Those  waves  which  are  of 
the  right  length  to  affect  the  eye  are  called  light. 

When  a  piece  of  iron  becomes  hot  enough,  it  gets  luminous; 
in  other  words,  it  gives  off  light.  The  molecules  of  the  iron 
vibrate  very  rapidly,  and  this  vibration  sets  up  waves  in 
the  ether,  which  are  transmitted  in  all  directions.  These 
waves  we  call  light. 

91 


92 


LIGHT 


108.  Propagation  of  Light  Waves.  —  Just  how  the  ether 
transmits  these  waves  is  still  a  mystery,  but  it  is  known  that 
they  are  transverse,  and  that  they  travel  in  straight  lines. 

109.  Velocity   of  Light.  —  It   is   easy   to   find   examples 
showing  that  sound  takes  time  to  travel,  but  all  ordinary 
examples  fail  to  show  that  the  same  is  true  of  light,  and 
for  many  centuries  the  transmission  of  light  was  thought 
to  be  instantaneous. 

110.  Roemer's  Method  of  Finding  Velocity  of  Light.  — 
The  first  man  to  prove  that  the  passage  of  light  requires 
time  was  Roemer,  and  he  did  it  by  accident. 


FIGURE  68.  —  RELATIVE  POSITIONS  OF  SUN,  EARTH,  JUPITER, 
AND  MOON  OF  JUPITER. 

Roemer  was  an  astronomer  who  lived  during  the  seven- 
teenth century.  About  1676  he  was  studying  the  eclipses 
of  one  of  the  moons  of  Jupiter  by  Jupiter.  He  found  that 
the  eclipses  did  not  occur  at  regular  intervals,  as  was  ex- 
pected, but  that  for  six  months  the  time  between  eclipses  be- 
came shorter  and  shorter,  and  then  for  the  next  six  months 
it  became  longer  and  longer.  (Figure  68  shows  the  relative 
position  of  the  heavenly  bodies  under  consideration.) 

Every  time  the  moon  of  Jupiter  came  into  the  shadow 
of  Jupiter,  there  was  an  eclipse.  Roemer  knew  how  long 


COMPARATIVE   VALUE  OF   VELOCITY  OF  LIGHT     93 

it  took  the  moon  to  make  a  complete  revolution  about 
Jupiter,  and  so  assumed  that  eclipses  ought  to  come  at  that 
interval.  He  made  a  schedule  something  like  the  follow- 
ing (assuming  that  it  takes  exactly  30  days  for  the  moon  to 
make  a  revolution)  : 

1st  eclipse 12  o'clock  Jan.     1 

2d  eclipse 12  o'clock  Jan.  31 

3d  eclipse  12  o'clock  Mar.    1 

4th  eclipse 12  o'clock  Mar.  31 

5th  eclipse 12  o'clock  Apr.  30 

6th  eclipse  .     . ' 12  o'clock  May  30 

7th  eclipse \  12  o'clock  June  29 

8th  eclipse 12  o'clock  July  29 

9th  eclipse  . 12  o'clock  Aug.  28 

10th  eclipse  12  o'clock  Sept.  27 

llth  eclipse  12  o'clock  Oct.  27 

12th  eclipse 12  o'clock  Nov.  26 

13th  eclipse 12  o'clock  Dec.  26 

The  earth  being  at  E,  at  the  time  of  the  first  eclipse, 
Roemer  found  that  at  each  occurrence  the  eclipses  were 
behind  the  schedule  more  and  more,  and  that  six  months 
later,  when  the  earth  was  at  E2,  the  eclipse  occurred  1000 
seconds  later  than  the  scheduled  time  (12  o'clock,  June  29). 
Then,  for  the  next  six  months,  the  eclipses  began  to  catch 
up  with  the  schedule,  and  were  exactly  on  time  (12  o'clock 
Dec.  26)  when  the  earth  got  back  to  EI. 

Roemer  then  reasoned  that  it  took  the  light  1000  seconds 
to  cross  the  earth's  orbit,  a  distance  of  186,000,000  miles. 

1  SA  onn  nnn 
This  gave  the  velocity  of  light  as  —    T— ^ =  186.000  miles 

per  second. 

111.  Comparative  Value  of  Velocity  of  Light.  —  The 
velocity  of  light,  186,000  miles  per  second,  is  so  great  that 
the  mind  cannot  appreciate  it  without  some  comparative 


94  LIGHT 

values.  It  means  that  a  ray  of  light  would  travel  nearly 
7J  times  around  the  earth  in  one  second.  It  would  take  a 
train,  going  at  60  miles  an  hour,  over  4  months  to  travel 
as  far  as  a  ray  of  light  can  travel  in  one  second. 

112.  Shadows.  —  Since  light  travels  in  straight  lines  and 
will  not  go  through  opaque  objects,  it  is  easily  shut  off  by 
putting  one  of  these  objects  in  its  path.  When  light  is 
shut  off  from  a  certain  space  by  an  object  placed  in  the 
path  of  the  light,  that  space  is  called  a  shadow.  A  shadow 
is  the  space  from  which  the  light  has  been  cut  off. 

A  man  walking  on  the  sidewalk  on  a  sunny  day  casts  a 
shadow.  Hold  your  hand  in  front  of  a  lamp  and  your  hand 
casts  a  shadow.  The  earth  shuts  off  part  of  the  sun's  rays 
and  casts  a  shadow. 

The  shadow  in  each  of  these  cases  is  the  space  back  of 
the  object.  It  is  not,  as  we  often  think,  the  dark  portion 

of  the  sidewalk  or  of  the 
wall.  Those  are  only  cross 
sections  of  the  shadows. 

113.   Shadow  from  a  Point 
Source    of    Light.  —  Figure 

FIGURE  69.-  SHADOW  FROM  A  POINT     69   sh°WS   a  shadow  Cast   b>' 
SOURCE  OF  LIGHT.  an  object   in   front  of   light 

coming  from  a  point  source. 

The  light  travels  out  in  all  directions  from  point  P,  but 
that  which  strikes  the  rectangle  abed  is  shut  off,  thus  making 
the  space  S  without  light,  or  a  shadow.  The  shadow,  then, 
is  a  pyramid  with  the  top  cut  off. 

Had  the  object  been  circular,  the  shadow  would  have 
been  a  cone  with  the  top  cut  off. 

114.  Shadow  from  a  Large  Source.  —  Most  of  our  light 
comes  from  large  sources  and  not  from  points.  Figure  70 


SHADOW   FROM  A   LARGE  SOURCE  95 

shows  the  shadow  cast  by  an  object  (0)  with  a  large  source 
of  light  (S). 

It  will  be  seen  that  the  space  above  be  and  below  ad  is 
lighted  by  all  of  S.  The  space  between  ac  and  bd  beyond 
the  object  gets  no  light  at  all,  and  so  is  totally  dark.  This 
is  called  the  umbra  (  U).  The  space  outside  the  umbra, 


FIGURE  70. — SHADOW  FROM  a  LARGE  SOURCE  OF  LIGHT. 

and  still  inside  ad  and  be,  is  called  the  penumbra  (P,  P). 
This  space  is  totally  dark  at  ac  and  bd,  but  becomes  lighter 
and  lighter,  as  you  go  outwlard.  That  is,  point  y  has  more 
light  than  point  x,  because  more  of  S  is  shining  on  it. 

Shadows  play  a  great  part  in  the  arts  both  of  painting 
and  of  sculpture.  They  also  enter  into  the  problems  of 
proper  illumination,  and  so  will  be  further  discussed  under 
that  topic. 


CHAPTER  IX 


REFLECTION    AND    MIRRORS 

115.  Reflection.  —  If  a  ray  of  light  strikes  a  bright  sur- 
face, it  will  be  partially  reflected.     Reflection  is  the  returning 
cf  a  ray  of  light  into  the  same  medium  from  which  it  came, 
when  it  strikes  another  medium. 

One  of  the  most  common  cases  of  reflection  is  seen  when 
a  ray  of  light  strikes  a  mirror.     Figure  71  shows  a  ray  of 

light  striking  a  mirror  and  being 
reflected. 

IR  is  the  incident  ray.  RR  is 
the  reflected  ray.  MM  is  the 
mirror,  and  OP  is  the  perpen- 
dicular to  the  mirror  at  the  point 
where  the  ray  IR  strikes  the 
mirror. 

The  angle  between  the  incident 
ray  and  the  perpendicular  to  the 
mirror  is  called  the  angle  of  in- 
cidence. 

The  angle  between  the  reflected  ray  and  the  perpendicular  to 
the  mirror  is  called  the  angle  of  reflection. 

Light  is  always  reflected  so  that  the  angle  of  reflection  equals 
the  angle  of  incidence.     This  is  called  the  Law  of  Reflection. 

116.  Pencil  of  Rays.  —  So  far  we  have  spoken  of  rays  of 
light.     Light  never  goes  in   single  rays,  but  in  bunches  of 

96 


M 


FIGURE  71*.  —  SHOWING  REFLEC- 
TION OF  A  RAY  OF  LIGHT. 


IMAGE  IN  A   PLANE  MIRROR 


97 


rays.     A  small  bunch  of  rays  is  called  a  pencil  of  rays,  and 

this  is  what  we  have  to  consider  instead  of  single  rays.     A 

person    gets    a    pencil    of 

rays,  or  many  pencils  of 

rays,   in  his  eye,   instead 

of    just    single    rays. 

(Figure  72.) 

117.   Image  in  a  Plane 
Mirror.  —  Figure  73  shows 
the  image  in  a  plane  mirror, 
mirror ;  and  a'bf ',  the  image. 


FIGURE  72.  —  A  PENCIL  OF  RAYS. 


The  object  is  ab ;  MM,  the 
An  image  is  the  space  occupied 
by  what  is  apparently  the  object  itself. 

Rays  are  sent  off  in  all  directions  from  each  point  of  the 
object.  Let  us  consider  the  two  points  a  and  b,  the  head 
and  tail  of  the  object.  There  is  just  one  pencil  of  rays  from 

each  of  these  points 
which  goes  out,  strikes 
the  mirror  at  the  right 
angle,  and  is  reflected 
into  the  eye. 

The  pencil  of  rays 
coming  from  a,  after 
being   reflected    at  c, 
appears  to  come  from 
point    a' ;      and    the 
pencil  of.  rays  coming 
from    6,    after    being 
reflected  at  d,  appears 
to     come     from     b'. 
By  geometry  it  is  easily  proved  that  the  image  is  as  far 
back  of  the  mirror  as  the  object  is  in  front,  and  on  a  line  with 
the  object,  perpendicular  to  the  mirror. 


M 


FIGURE  73.  —  CONSTRUCTION  OF  AN  IMAGE  IN 
A  PLANE  MIRROR. 


98  REFLECTION  AND   MIRRORS 

There  are  two  kinds  of  images,  real  and  virtual '. 

A  real  image  is  an  image  through  which  the  rays  of  light 
actually  pass. 

A  virtual  image  w  an  image  through  which  the  rays  of  light 
apparently  pass,  but  do  not. 

It  will  be  seen  by  these  definitions  that  the  image  in  a 
plane  mirror  is  virtual.     Why? 

118.   Concave   Mirrors.  —  A   concave  mirror  is  a  mirror 
which  curves,  and  has  the  hollow  side  towards  the  object. 

There  are  several  kinds  of  concave 
mirrors.     The  two  most  common  ones 

Ci 

are  the  spherical  mirror  (Figure  74)  and 
the  parabolical  mirror  (Figure  75). 


FIGURE  74  -A  SPHERI-       The  spherical  mirror  is  a  portion  of 
CAL  MIRROR. 

the  surface  of  a  sphere,  every  point  of 

which  is  equidistant  from  one  point  (c)  called  the  center  of 
curvature. 

The  parabolical  mirror  is  the  portion  of  the  surface  of  a 
paraboloid   and   is  of  the  shape  shown 
in  Figure  75.     The  parabolical  mirror  is 
much  better  than  the  spherical  because 
it  gives  a  perfect  image,  while  the  other 

does  not.  FlGURE  75-~  A  PARA~ 

BOLICAL  MIRROR. 
119.   Meaning  of  Terms.  —  In  Figure 

76  the  point  c  is  the  center  of  curvature,  and  is  equidistant 
from  all  points  in  the  surface  of  a  spherical  mirror.     The 

line    XO  is  the  prin- 
cipal axis,  and  is  the 

*- x     line    passing    through 

the  center  of  curvature 

FIGURE  76. -THE  PRINCIPAL  POINTS  OF  A       «    and    the   Center   °f 
SPHERICAL  MIRROR.  the  mirror  (0). 


IMAGE  IN  A   CONCAVE  MIRROR 


99 


The  focus  of  a  mirror  is  the  point  at  which  the  image 
is  located.  The  point  /  is  the  principal  focus,  and  is 
the  point  at  which  all  rays  parallel  to  the  principal 
axis  are  focused.  The  principal  focus  is  located  at  one 
half  the  distance  from  c  to  0.  The  focal  length  is  the  dis- 
tance (Of)  from  the  center  of  the  mirror  to  the  principal 
focus. 

120.  Image  in  a  Concave  Mirror.  —  Figure  77  shows  the 
construction  of  an  image  in  a  concave  mirror. 

First,  draw  ad  from  a,  the  head  of  the  object,  parallel 
to  the  principal  axis.  Since  this  is  a  ray  parallel  to  the 


FIGURE  77.  —  CONSTRUCTION  OF  IMAGE  IN  A  CONCAVE  MIRROR. 

principal  axis,  it  must  be  reflected  through  the  principal 
focus  /.  This  determines  line  dx. 

Second,  draw  ag  from  a  through  the  center  of  curvature  c. 
This  ray  is  reflected  back  upon  itself,  since  it  strikes  the 
mirror  perpendicularly.  The  point  a',  where  these  two 
reflected  rays  meet,  is  the  head  of  the  image. 

Third,  locate  the  tail  of  the  image  in  the  same  way.  This 
completes  the  construction  of  the  image. 

This  image  is  seen  to  be  real,  inverted,  and  smaller  than  the 
object.  The  image  may  be  located  by  this  method  for  any 
position  of  the  object.  The  description  of  the  image  can 
then  be  easily  given  from  the  figure. 


100         REFLECTION  AXD  MIRRORS 

121.  Convex    Mirrors.  —  A    convex    mirror    is    a    curved 
mirror  which  has  the  hollow  side  of  the  curve  away  from  the 
object. 

The  same  terms,  focus,  axis,  etc.,   apply  to   the  convex 
mirror  as  to  the  concave  mirror. 

122.  Image  in  a  Convex  Mirror.  —  The  construction  of 
the  image  in  a  convex  mirror  is  the  same  as  for  the  concave 
mirror.     Draw  the  two  lines  from  the  head  of  the  object, 


lb 
FIGURE  78. —  CONSTRUCTION  OF  IMAGE  IN  A  CONVEX  MIRROR. 

one  (ad,  Figure  78)  parallel  to  the  principal  axis,  and  the 
other  (ac)  through  the  center  of  curvature.  When  reflected, 
these  two  rays  pass  through  the  principal  focus  and  back  upon 
themselves,  respectively.  Where  they  meet  (a'}  is  the 
image  of  the  head.  The  image  of  the  tail  (br)  is  located  in 
a  similar  manner. 

In  this  case  the  image  is  virtual,  erect,  and  smaller  than  the 
object. 

123.  Applications  of  Mirrors.  —  1.  Plane  Mirror.  The 
general  use  of  the  plane  mirror  as  a  looking  glass  is  too 
familiar  to  need  discussion. 

2.  Concave  Mirror.  The  most  general  use  of  the  concave 
mirror  is  that  of  a  reflector.  Since  all  parallel  rays  come 
together  at  the  principal  focus,  it  is  seen  that  the  rays  from 
a  source  of  light  placed  at  the  principal  focus  will  be  sent 
out  as  parallel  rays.  (Figure  79.) 


APPLICATIONS  OF    lf/&jR(p«S^;  :  101 

The  automobile  headlight  is  an  example  of  this.  The 
bulb  is  so  placed  that  the  filament  of  the  lamp  is  very  near 
the  principal  focus  of  the  reflector.  This  sends  the  rays 
out  in  nearly  parallel  beams.  The  correct  position  of  the 
filament  is  just  beyond  the  principal  focus,  but  close  to  it. 
This  makes  the  rays  cross  and  then  diverge  slightly,  so  that 
a  large  area  of  the  road  can  be  seen.  The  same  use  is  also 
made  in  many  different  kinds  of  lamps. 

The  concave  mirror  is  used  in  all  telescopes  of  the  re- 
flector type.  The  largest  telescope  of  this  sort  has  just 
been  completed  by  the  Warner  Swazey  Company,  of  Cleve- 
land, to  be  used  at  the  Canadian  observatory  at  Victoria. 


FIGURE  79.  —  A  CONCAVE  MIRROR  USED  AS  A  REFLECTOR. 

The  concave  mirror  for  this  telescope  is  72  inches  in  diameter, 
and,  like  all  high-grade  concave  mirrors,  is  of  the  parabolical 
shape.  The  telescope  will  be  used  to  take  photographs  of 
distant  stars.  The  mirror  is  large  so  that  many  rays  of  the 
star  are  focused  at  the  image. 

3.  Convex  Mirror.  The  convex  mirror  is  often  used  on 
automobiles  to  give  the  driver  a  view  of  vehicles  behind 
him.  It  is  usually  placed  on  the  front  fender  or  attached 
to  the  side  of  the  windshield.  The  mirror  gives  a  small 
but  clear  image  of  everything  in  the  rear. 

Large  spheres  with  mirror  surfaces  are  often  placed  in 
flower  gardens  to  add  to  the  decorations  and  to  give  beau- 
tiful images  of  the  walks  and  flowerbeds. 


102       \ily', '^tiEFLECTiON    AND   MIRRORS 


Another  use  of  the  convex  mirror  is  that  of  the  "  vanity- 
mirror  "  carried  in  ladies'  hand  bags  or  pocketbooks.  It  is 
much  preferred  to  the  plane  mirror,  for  even  a  small  one  an 
inch  in  diameter  will  give  an  image  of  the  whole  face. 


6  c 

FIGURE  80.  —  PECULIARLY  SHAPED  MIRRORS. 


4.  Peculiarly  Shaped  Mirrors.  There  are  many  peculiarly 
shaped  mirrors,  such  as  are  found  in  "  hilarity  halls,"  etc. 
Figure  80  shows  a  few  of  these.  Due  to  the  peculiar  shapes, 
the  images  are  distorted  and  afford  amusement  for  the 
patrons. 


CHAPTER  X 


REFRACTION  AND   LENSES 

124.  Refraction.  —  The    term    refraction    is    very    often 
confused  with  the  term  reflection,  but  it  must  be  borne  in 
mind  that  the  two  mean  entirely  different  things. 

Refraction  is  caused  by  the  change  in  velocity  of  a  ray  of 
light  when  it  passes  from  one  medium  to  another.  This  causes 
a  bending  of  the  ray  when  it  strikes  at  an 
angle  other  than  90°. 

If  a  lead  pencil  be  put  into  a  beaker  of 
water  (Figure  81),  it  looks  as  if  the  lead 
pencil  were  bent  at  the  water  line.  If  you 
try  to  touch  an  object  under  water  very 
quickly,  your  hand  will  pass  over  the  object, 

showing  that  the  object  appears  higher  than 

•j.        11     •         TJ>  11,11  i      FIGURE  81.  —  A 

it  really  is.     It  you  look  through  a  poor  grade       PENCIL  LOOKS 

of  window  glass  at  some  straight  line,  such 
as  the  side  of  a  tall  chimney,  the  line  looks 
jagged  and  crooked.  (Figure  82.) 

All  these  illusions  are  caused  by  refraction. 

125.  Refraction  Explained.  —  Figure  83  shows  a  ray  of 
light  (A)  passing  from  air,  through  a  piece  of  plate  glass, 
back  into  air. 

The  small  lines  ab  represent  the  wave  front  of  the  ray. 
A  ray  of  light  always  travels  at  right  angles  to  its  wave 
front ;  so  the  wave  front  determines  its  direction. 

103 


BENT  AT  THE 
SURFACE  OF 
THE  WATER. 


104 


REFRACTION    AND    LENSES 


The  ray  travels  in  a  straight  line  until  it  strikes  the 
glass.  The  side  a  strikes  first,  and  so  is  retarded,  since 

light  cannot  travel  in 
glass  as  fast  as  in  air. 
This  allows  b  to  swing 
ahead,  since  it  is  still  in 
air.  This  continues  until 
both  a  and  b  are  inside  the 
glass.  Then  they  again 
go  at  equal  speeds,  giving 

FIGURE  82. -A  CHIMNEY  VIEWED  THROUGH  the  TW  a  straight  path, 
POOR  WINDOW  GLASS.  but  one  slightly  deviated 

from  its  original  path. 

At  the  other  side  of  the  glass,  a  comes  to  the  surface 
first,  and  so  swings  ahead  of  6,  for  it  now  travels  in  air. 
It  continues  to  do  this  until  both  a  and  b  are  again  in  air. 
Here  they  continue  again  at  equal  speeds,  and  the  ray 
again  goes  in  a  straight  line. 

If  the  two  sides  of  the  glass  are  parallel,  the  ray  swings 
back  just  as  much  as  it  deviated  in  the  first  place.  This 
makes  its  path  parallel  to  its  path  before  entering  the  glass, 
but  not  in  the  same  line. 

If  the  two  sides  of  the  glass  are  not  parallel,  the  ray 
will  not  be  parallel  with  its  first  path,  but  will  deviate  ac- 
cording to  the  angle  of  the  two  surfaces. 

126.  Meaning  of  Terms  and  Law  of  Refraction.  —  In 
refraction.,  the  incident  ray  is  the  ray  before  it  strikes  the 
refracting  surface  (AO  for  the  first  surface,  and  00'  for  the 
second  surface,  Figure  83). 

The  refracted  ray  is  the  ray  after  it  strikes  the  refracting 
surface  (00'  for  the  first  surface,  and  0' A'  for  the  second 
surface) . 


INDEX  OF   REFRACTION 


105 


The  angle  of  incidence  is  the  angle  between  the  incident 
ray  and  the  perpendicular  to  the  surface  (angle  i  for  the 
first  surface,  and  angle  i'  for  the  second  surface). 

The  angle  of  refraction  is  the  angle  between  the  refracted 
ray  and  the  perpendicular  to  the  surface  (angle  r  for  the 
first  surface,  and  angle  r'  for  the  second  surface). 


FIGURE  83.  — DIAGRAM  EXPLAINING  REFRACTION  OF  LIGHT. 


The  law  of  refraction :  A  ray  of  light  passing  from  a  rare 
medium  into  a  denser  medium  always  bends  toward  the  per- 
pendicular, and  a  ray  of  light  passing  from  a  dense  to  a  rarer 
medium  always  bends  away  from  the  perpendicular. 

127.  Index  of  Refraction.  —  Different  substances  refract 
light  in  varying  degrees.  In  order  to  compare  and  express 
these  amounts  of  refraction  a  term  called  index  of  refraction 
is  used. 


106  REFRACTION   AND   LENSES 

The  index  of  refraction  is  equal  to  the  velocity  in  the  rare 
medium  divided  by  the  velocity  in  the  dense  medium. 

Index  of  Refraction  =  — 

Vdense 

There  are  two  kinds  of  indexes  of  refraction,  relative  and 
absolute. 

The  relative  index  of  refraction  is  the  index  when  the  ray 
passes  from  one  substance  to  another,  and  is  correct  for  those 
two  substances  only. 

The  absolute  index  of  refraction  is  the  index  when  the  ray 
passes  from  a  vacuum  into  a  substance,  and  applies  to  that 
one  substance  only. 

The  index  of  refraction  is  used  principally  in  the  manu- 
facture of  lenses.  The  index  determines  the  amount  of 
curvature  that  the  lens  must  have.  It  is  the  high  index  of 
refraction  of  the  diamond  that  gives  it  its  sparkle. 

128.  Applications  of  Refrac- 
tion. —  The  applications  of  re- 
fraction are  used  in  lenses  and 
prisms.  These  will  be  discussed 
later. 

We  have  mentioned  the  effect 
of  looking  at  a  straight  line 

through  a  poor  grade  of  window 

FIGURE  84. -REFRACTION  OF  LIGHT     ]ags       Explain  this> 
ABOVE  A  HOT  STOVE. 

It  is  a  common  thing  to  notice 

the  wavy  effect  above  a  fire  or  stove  (Figure  84).  This  is 
not  heat  waves,  as  so  many  think ;  but  it  is  due  to  refrac- 
tion. The  air  above  the  fire  is  heated  and  becomes  less 
dense  than  the  surrounding  air.  Light  rays  passing  through 
these  layers  of  air  of  unequal  densities  are  refracted,  giving 
the  wavy  effect.  . 


CRITICAL  ANGLE 


107 


Our  atmosphere  acts  as  a  refracting  substance  to  the 
sun's  rays.     For  this  reason  we  can  actually  see  the  sun 


Evening 


FIGURE  85.  —  REFRACTION  OF  LIGHT  BY  THE  EARTH'S  ATMOSPHERE. 

before  it  is  above  the  horizon  in  the  morning,  and  also  after 
it  has  gone  below  the  horizon  in  the  evening.     (Figure  85.) 

129.  Critical  Angle. - 
Figure  86  shows  what 
takes  place  when  a  ray 
of  light  passes  from  a 
dense  medium,  such  as 
water,  to  a  rare  medium, 
such  as  air. 

A  ray  of  light  AO  passes 
from  the  dense  medium 
and  goes  into  the  rare 
medium  at  0.  According 
to  the  law  of  refraction, 

the  ray  is  bent  away  from 

,1  vi  r>rtr  FIGURE  86.  —  DIAGRAM  EXPLAINING 

the     perpendicular     PP  ,  CRITICAL  ANGLE. 

making   the   angle   of   re- 
fraction r  larger  than  the  angle  of  incidence  i.     (Figure  86.) 
Now,  if  the  angle  of  incidence  is  made  larger  and  larger, 
the  angle  of  refraction  will  become  larger  and  larger  also 


108 


REFRACTION   AND   LENSES 


and  will  always  be  greater  than  its  corresponding  angle  of 
incidence. 

If  the  angle  of  incidence  becomes  large  enough  (i?),  the 
angle  of  refraction  (r2)  becomes  equal  to  90°,  and  the  re- 
fracted ray  passes  out  along  the  surface  of  the  dense  medium 
(OB').  The  angle  of  incidence  is  then  called  the  critical 
angle. 

The  critical  angle  is  an  angle  of  incidence  which  corresponds 
to  an  angle  of  refraction  of  90°. 

130.  Total  Reflection.  —  Angle  i  (Figure  87)  is  the 
critical  angle,  and  so  the  refracted  ray  OA'  passes  out 

along  the  surface  of  the 
dense  medium,  making 
the  angle  of  refraction  (r) 
equal  to  90°. 

Now,  if  the  angle  of 
incidence  is  made  still 
larger,  such  as  i,  the 
angle  of  refraction  be- 
comes greater  than  90°. 
This  makes  the  refracted 
ray  return  into  the  same 
medium  in  which  it  en- 
tered. But  this  is  reflec- 
tion instead  of  refraction, 

and  so  the  ray  must  obey  the  law  of  reflection,  making  the 
angle  of  reflection  (r2)  equal  to  the  angle  of  incidence  (i^). 

This  is  called  total  reflection,  because  none  of  the  rays 
can  be  refracted,  but  all  are  reflected. 

Total  reflection  is  reflection  against  a  surface  of  a  rare 
medium  when  the  angle  of  incidence  is  greater  than  the  critical 
angle. 


FIGURE  87.  —  DIAGRAM  EXPLAINING 
TOTAL  REFLECTION. 


PRISMATIC   WINDOW  GLASS 


109 


FIGURE  88.  —  POSITIONS  OF  PRISMS  IN  A 
LIGHTHOUSE  REFLECTOR. 


It  must  be  noted  that  total  reflection  takes  place  only 
when  the  ray  is  passing  from  a  dense  to  a  rare  medium. 

APPLICATIONS  OF  TOTAL  REFLECTION 

131.  The    Lighthouse    Reflector.  —  The    lighthouse    re- 
flector is  an  application  of  total  reflection.     The  source  of 
light,    a    gas    flame 

or   an   electric   light 

bulb,    is    placed    at 

the     center.       (L, 

Figure  88.)    Circular 

right-angled     prisms 

(Figure     89)     are 

placed     around    the 

light  at  P,  P,  P,  etc. 

(Figure  88),  forming 

an  inclosed  sphere.     Instead  of  the  prisms  being  far  apart, 

as  in  the  figure,  they  are  placed  so  close  together  that  no 

light  gets  out  between  them. 

The  light  coming  from  the  center 
strikes  one  leg  of  the  right-angled 
prism,  enters  the  glass,  and  then 

FIGURE  89.  — A  LIGHT-     strjkes    the    hypotenuse    at    an    angle 

HOUSE  REFLECTOR  PRISM. 

greater  than  the  critical  angle.  Total 
reflection  takes  place,  and  all  the  light  is  sent  out  in  a 
parallel  beam.  By  this  means  all  the  light  is  utilized,  top, 
bottom,  and  sides. 

132.  Prismatic  Window   Glass.  —  Very   often   it   is   im- 
possible by  means  of  the  ordinary  windows  to  get  sunlight 
into  rooms  shaded  by  other  buildings,  especially  in  large 
cities  where  "  skyscrapers  "  are  the  rule.     Prismatic  window 
glass  helps  to  do  away  with  this  difficulty.     The  light  com- 


110 


REFRACTION   AND   LENSES 


ing  almost  straight  down  (Figure  90)  strikes  the  prismatic 

glass  and  is  totally  reflected  into  the  room. 

133.  Field  Binocu- 
lars. —  In  the  field 
binoculars,  such  as 
are  used  by  officers 
of  the  army  and 
navy,  the  light  must 
pass  a  distance  of 
several  inches  after 
it  enters  the  instru- 
ment before  it  reaches 
the  eye.  To  keep 
the  instrument  from 
becoming  too  long, 
the  rays  of  light  are 
reflected  back  and 
forth  from  one  end 

to     the     other     by 

FIGURE  90.  —  USE  OF  PRISMATIC  WINDOW  «        .     ,    ' 

GLASS.  means    of    right- 

angled  prisms. 

Figure  91  shows  a  diagram  of  the  path  of  a  light  ray  in 
one  tube  of  the  binocular. 

134.  A  Fish's  View  of  the  Outside  World.  —  It  is  rather 
interesting  to  note  just 
how  the  outside  world 
looks  to  the  fish  below 
the  surface  of  the 
water.  Figure  92  is  a 
diagram  showing  how 
the  rays  of  light  come  to  the  fish's  eye. 

The  sky  and  all  objects  above  the  horizon  are  seen  through 


FIGURE  91.  — TOTAL  REFLECTION  USED  IN 
THE  BINOCULARS. 


LENSES 


111 


a  cone  whose  angle  is  about  97°.  Outside  of  this  cone  the 
fish  gets  rays  coming  from  the  bottom  and  reflected  at  the 
surface  of  the  water.  This  makes  the  sky  look  as  if  it  had 
a  fringe  of  stones  or 
grass,  according  to 
whether  the  bottom 
is  stony  or  grassy.  _ 

135.  The  Diamond. 
—  As    mentioned    be- 
fore,   the    large    index 

FIGURE  92.  —  A  FISH'S  VIEW  OF  THE 
of  refraction  in  a  dia-  OUTSIDE  WORLD. 

mond      gives     it     its 

sparkle.  As  the  diamond  has  a  large  index  of  refraction 
and  is  cut  with  many  facets,  the  light  is  reflected  many 
times  within  the  stone,  so  that  there  is  scarcely  an  angle 
at  which  you  can  view  it  without  getting  a  flash  of  light. 

LENSES 

136.  Lenses.  —  A  lens  is  a  transparent  body  of  such  a 
shape  that  it  will  focus  rays  of  light.     There  are  two  general 

classes  of  lenses  :  (a)  con- 
verging, (b)  diverging. 

A  converging  lens  is  a 
lens  which  tends  to  bring 
the  rays  together  after  they 
pass  through.  (Figure 
93.) 

A  diverging  lens  is  a 
lens  which  tends  to  send  the  rays  farther  apart  after  they  go 
through.  (Figure  94.) 

Lenses   are   of   different   shapes   and   are   given   specific 
names  according  to  these  shapes.     (Figure  95.)     In  general, 


FIGURE  93. —  LIGHT  PASSING  THROUGH  A 
CONVERGING  LENS. 


112 


REFRACTION   AND   LENSES 


lenses  that  are  thicker  at  the  center  than  at  the  edges  are 
converging,  while  those  thinner  at  the  center  than  at  the 
edges  are  diverging. 

137.  Meaning  of  Terms.  —  The 
line  drawn  through  the  centers  of 
curvature  of  the  two  surfaces  is 
called  the  principal  axis.  (CC, 
Figure  96.) 

The  optical  center  (0)  is  the  point 
on  the  principal  axis,  midway  be- 
tween the  surfaces  of  the  lens. 

The   principal  focus    (F)    is   the 
point  at  which  all  rays  parallel  to 
the  principal  axis  are  focused. 

The  focal  length   (OF)   is  the  distance  from  the  optical 
center  to  the  principal  focus. 

The  image  is  a  point,  or  a  series  of  points,  at  which  the 
rays  coming  from  an  object  are  focused.     The  rays  coming 


FI.GURE    94.  —  LIGHT    PASS- 
ING THROUGH   A  DIVERGING 

LENS. 


c  d  c  f 

FIGURE  95. —  DIFFERENT  SHAPED  LENSES. 

from  one  point  of  the  object  are  focused  at  one  point  in  the 
image. 

138.  Image  through  a  Converging  Lens.  —  There  are 
five  possible  settings  for  a  converging  lens : 

I.    The  object  beyond  2  F. 


IMAGE   THROUGH  A    CONVERGING  LENS        113 


To  construct  the  image  for  this  position  (Figure  97) 
draw  the  lens  and  the  principal  axis;  locate  the  optical 
center  and  the  principal  focus.  (Note:  Every  lens  has  its 
own  focal  length ;  and  if  this  is  given,  the  principal  focus 
can  be  located  by  it;  but  if  the  focal  length  is  not  given, 
then  a  focal  length 
must  be  assumed.) 
Next,  mark  off  F 
and  2  F  on  both  sides 
of  the  lens,  and  place 

'  *  FIGURE  96.  —  PRINCIPAL  POINTS  OF  A  LENS. 

the  object  beyond  2  F. 

Now,  there  are  an  infinite  number  of  rays  passing  from 
every  point  of  the  object,  but  two  rays  are  sufficient  to 
locate  the  image  of  any  one  point.  Select  the  two  rays, 
one  of  which  is  parallel  to  the  principal  axis,  and  the  other 
which  passes  through  the  optical  center. 

To  locate  the  head  of  the  image  draw  these  two  rays, 
the  one  parallel  to  the  axis  passes  through  the  principal 


Object 


FIGURE  97.  —  CONSTRUCTION  OF  IMAGE  WHEN  OBJECT  is  BEYOND  2  F. 

focus  F  (because  all  parallel  rays  are  focused  at  this  point), 
and  the  one  through  the  optical  center  passes  on  through 
the  lens  in  a  straight  line  (it  really  zigzags  just  a  little  at 
the  lens).  The  point  at  which  these  two  rays  meet  is  the 
image  of  the  head. 


114 


REFRACTION    AND    LENSES 


In  the  same  way  the  tail  of  the  image  is  located,  thus 
locating  the  whole  image. 

The  description  of  an  image  gives  four  things:  (1)  posi- 
tion, (2)  size,  (3)  whether  it  is  erect  or  inverted,  (4)  whether 
it  is  real  or  virtual. 

When  the  object  is  beyond  2  F,  the  image  is  (1)  between  F 
and  2  F,  (2)  smaller  than  the  object,  (3)  inverted,  and  (4)  real. 

II.    The  object  at  2  F. 

To  construct  the  image  with  the  object  in  this  position, 
proceed  exactly  as  in  the  former  case.  (Figure  98.) 


Object 


V 


FIGURE  98.  —  CONSTRUCTION  OF  IMAGE  WHEN  OBJECT  is  AT  2  F. 

The  image  is  (1)  at  2  F,  (2)  of  the  same  size  as  the  object, 
(3)  inverted,  and  (4)  real. 

III.    The  object  between  F  and  2  F. 

Construct  as  before.  (Figure  99.)  The  image  is  (1)  be- 
yond 2  F,  (2)  larger  than  the  object,  (3)  inverted,  and  (4)  real. 


Object 


FIGURE  99.  —  CONSTRUCTION  OF  IMAGE  WHEN  OBJECT  is  BETWEEN 

F  AND    2  F. 


IMAGE  THROUGH  A  CONVERGING  LENS    115 

IV.    The  object  at  F. 

Construct  as  before.  (Figure  100.)  The  rays  after  passing 
through  the  lens  are  parallel,  and  so  never  meet.  There- 
fore there  is  no  image. 


FIGURE  100. — -CONSTRUCTION  OF  IMAGE  WHEN  OBJECT  is  AT  F. 

V.    The  object  between  F  and  the  lens. 

The  construction  is  the  same  as  before,  except  that  the 
rays  after  passing  through  the  mirror  diverge,  and  so  have 


FIGURE  101.  —  CONSTRUCTION  OF  IMAGE  WHEN  OBJECT  is  BETWEEN  F 
AND  THE  LENS. 

to  be  produced  backward  to  determine  the  point  where  they 
meet.     (Figure  101.) 


116  REFRACTION   AND   LENSES 

The  image,  then,  is  (1)  on  the  same  side  of  the  lens  as  the 
object,  (2)  larger  than  the  object,  (3)  erect,  and  (4)  virtual. 

139.  Image  through  a  Diverging  Lens.  —  There  were 
five  distinctive  positions  for  the  object  in  the  case  of  the 
converging  lens,  but  for  the  diverging  lens  there  is  only  one. 
The  image  may  be  constructed  in  a  similar  manner  to  those 
already  studied. 

Draw  the  two  rays  from  each,  the  head  and  tail  of  the 
object.  (Figure  102.)  The  two  rays  parallel  to  the  principal 
axis  diverge  at  such  an  angle  that,  if  produced,  they  pass 


Object 


FIGURE  102.  —  CONSTRUCTION  OF  IMAGE  THROUGH  A  DIVERGING  LENS. 

through  the  principal  focus.  These  produced  rays  meet 
the  rays  coming  from  the  same  points  and  form  an  image 
which  is  (1)  between  F  and  the  lens,  (2)  smaller  than  the 
object,  (3)  erect,  and  (4)  virtual. 

No  matter  where  the  object  is,  the  image  is  formed  as 
described  above.  If  the  object  is  a  great  distance  away, 
the  image  approaches  F ;  and  as  the  object  comes  closer  to 
the  lens,  the  image  also  comes  closer  to  the  lens,  and  gets 
larger.  The  image  reaches  the  lens  and  becomes  equal  to 
the  object  when  the  object  reaches  the  lens. 

APPLICATIONS  OF  LENSES 

140.  The  Pinhole  Camera.  —  The  simplest  camera  that 
we  have  is  illustrated  by  Figure  103.  It  consists  of  a  light= 


THE  LENS  CAMERA  117 

tight  box  with  a  pinhole  in  the  front.  A  sensitized  plate 
or  film  may  be  placed  at  the  back,  and  a  picture  can  be 
taken.  The  principle  of  the  pinhole  camera  is  this :  All 


FIGURE  103.  —  THE  PINHOLE  CAMERA. 

the  rays  allowed  to  pass  through  the  pinhole  from  the  same 
point  of  the  object  fall  at  the  same  point  at  the  back  of  the 
box.  A  series  of  these  points  forms  the  image. 

141.  The  Lens  Camera.  —  The  pinhole  camera  is  not 
satisfactory,  for  if  the  pinhole  is  very  small,  the  image  will 
be  very  weak  and  dim ;  and,  on  the  other  hand,  if  the  hole 


FIGURE  104.  —  THE  LENS  CAMERA. 

is  made  large,  then  the  rays  from  the  same  point  on  the 
object  fall  over  quite  an  area  of  the  image,  and  this  makes 
the  image  indistinct,  or  blurred. 

By  the  use  of  a  converging  lens,  Fig.  104,  the  opening  may 
be  made  large  and-,  at  the  same  time,  the  image  may  be 


118  REFRACTION   AND   LENSES 

kept  sharp  and  distinct.     This  is  an  application  of  the  con- 
verging lens  with  the  object  beyond  2  F. 

In  order  that  all  the  rays  coming  through  the  lens  from 
one  point  of  the  object  be  focused  at  a  single  point  of  the 


FIGURE  105.  —  THE  40-lNCH  TELESCOPE  AT  THE  YERKES  OBSERVATORY, 
UNIVERSITY  OF  CHICAGO,  WILLIAMS  BAY.  WISCONSIN. 

This   is   the    largest   refracting   telescope   in    existence.      The   tube   is 
•     64  ft.  long,  52  in.  in  diameter  at  the  center,   and  the  whole  in- 
strument weighs  75  tons. 


THE  EYE  119 

image,  the  lens  must  be  ground  with  great  care.  This  is 
why  the  best  cameras  are  so  expensive. 

The  plate  or  film  upon  which  the  picture  is  taken  is  a 
piece  of  glass  or  other  transparent  substance  covered  with  a 
gelatin.  This  gelatin  is  of  such  a  composition  that  when 
sun  light  strikes  it,  it  is  made  insoluble.  When  a  picture  is 
taken,  the  rays  from  the  light  parts  of  the  object  affect  the 
plate  more  than  the  rays  from  the  dark  parts.  Then,  when 
the  plate  is  "  washed  "  the  unaffected  parts  dissolve,  leaving 
the  insoluble  part  on  the  plate. 

The  plate  is  then  washed  in  a  "  fixing  "  solution,  which 
makes  the  remaining  gelatin  hard  to  scratch.  The  plate  is 
now  called  the  negative.  It  has  dark  spots  where  the  object 
is  light,  and  light  spots  where  the  object  is  dark. 

For  printing  the  pictures,  either  a  paper  or  glass  with  a 
sensitive  gelatin  is  used.  The  "  negative  "  is  laid  over  the 
sensitive  paper  or  glass  and  held  in  the  sun  for  a  short  time. 
The  sensitive  plate  is  affected  just  as  the  negative  was 
when  it  was  made,  except  that  the  dark  and  light  spots 
are  reversed,  thus  reproducing  the  object  as  it  was  seen. 

As  all  these  processes  must  be  done  with  painstaking 
care,  photography  is  quite  an  art. 

142.  The  Eye.  —  The  eye  is  also  an  application  of  the 
converging  lens  when  the  object  is  placed  beyond  2  F. 

The  human  eye  is  about  an  inch  in  diameter  and  has 
three  coats.  The  outer  coat  is  very  thick  and  strong,  and 
is  called  the  sclerotic  coat.  (Figure  106.)  This  sclerotic  coat 
covers  the  entire  eyeball,  but  at  the  front  it  is  transparent 
and  this  portion  has  the  name  cornea  (C). 

The  next  coat  (D)  is  dark  in  color,  and  is  called  the  choroid 
coat.  At  the  front,  the  choroid  coat  forms  a  kind  of  curtain, 
called  the  iris  (I).  The  iris  is  the  part  that  gives  color  to 


120 


REFRACTION   AND   LENSES 


FIGURE   106.  — THE  EYE. 


the  eye.     At  the  back  of  the  eye  is  a  third  coat  (R)  called 

the  retina.     This   is  nervous  tissue  composed    of   millions 

of  small  nerve  cells. 
These  cells  are  divided 
into  three  classes.  In 
one  class  are  those 
affected  by  red  light; 
in  another  class  are 
those  affected  by  green 
light;  and  the  third 
class  is  composed  of 
those  affected  by  blue 
light.  These  different 
kinds  of  cells  are  not 

in  separate  groups,  but  are  scattered  all  over  the  retina,  so 

that  every  point  has  all  three  kinds. 

At  the  front  of  the  eye,  fastened  into  the  choroid  coat, 

are  muscles  (m,  m). 

These  muscles  are  so  attached  that  they  stretch  or  relax 

a  small  membrane  sack  which  contains  the  crystalline  lens 

(C.  L.) .     This  crystalline  lens  is  a  transparent,  jelly-like  mass, 

and  is  a  true  lens. 

143.  How  We  See.  —  When  an  object  is  held  before  the 
eye,  an  image  is  focused  by  the  crystalline  lens  upon  the 
retina.     The  nerve  cells  are  affected  according  to  the  color 
of  the  light  which  falls  on  them.     Impulses  are  sent  to  the 
brain,  and  we  become  conscious  of  the  image. 

A  further  study  of  color  will  be  taken  up  later,  and  the 
subject  of  the  eye  should  then  be  reviewed. 

144.  Defective  Eyes.  —  There  are  many  defects  of  the 
eye,    but   we   will   mention    only    three :     short-sightedness 
(myopia),  long-sightedness  (hypermetropia),  and  astigmatism. 


DEFECTIVE   EYES 


121 


FIGURE   107. — A  SHORT-SIGHTED  EYE. 


Short-sightedness  is  caused  by  one,  or  both,  of  two  things. 

The  eyeball  is  too  long,  or  the  crystalline  lens  is  too  thick. 

When  the  image  falls 

in  front  of  the  retina, 

the    person    has    to 

bring  the  object  very 

near  the  eye   to   get 

the    image    to    move 

back  upon  the  retina. 

(Figure  107.) 
To  correct  this  defect,  diverging  lenses  should  be  used 

for  eye-glasses.     This  makes  the  image  fall  upon  the  retina 

when  the  object  is 
held  at  the  natural 
position.  (Figure 
108.) 

Long-sightedness  is 
just  the  opposite  of 
short-sightedness, 
and  is  caused  by 
just  the  opposite 

things.     The  eyeball  is  too  short,  or  the  lens  is  too  thin. 

This  makes  the  image  fall  back  of  the  retina,  so  that  it  is 

necessary  to  hold  the 

object    far    away   in 

order     to     get     the 

image  to  fall  on  the 

retina.       (Figure 

109.) 

Glasses  to  correct 

this  defect  should  be  converging  lenses.     (Figure  110.) 
Astigmatism  is  the  most  serious  of  the  three  defects,  and 


FIGURE  108. — A  SHORT-SIGHTED  EYE 
CORRECTED. 


FIGURE   109.  —  A  LONG-SIGHTED  EYE. 


122 


REFRACTION   AND    LENSES 


is  much  the  hardest  to  correct.     It  may  be  caused  by  several 
things,  such  as  irregularities  in  the  thickness  or  texture  of 

the  cornea,  or  in  the 
crystalline  lens. 
V         Figure    111     shows 
an  eye  with  irregular 
/    thickness       of       the 
cornea.      The    defect 
must  be  corrected  by 
having  glasses  ground 
to  fit  this  one  special 
Figure  112  shows  an  at- 


FIGURE   110. — A  LONG-SIGHTED  EYE 
CORRECTED. 


case,  and  this  requires  an  expert, 
tempt  to  correct  astigmatism. 
145.  The  Life-size  Picture 
Camera.  —  This  camera  is 
just  like  the  ordinary  camera 
except  that  the  box  is  very 
long  and  large  and  the  lens 
has.  a  greater  focal  length.  FlGURE  1 1  L  ~  AN  ^STIGMATIZED  EYE. 

This  is  an  application  of  the  second  position  of  the  con- 
verging lens.     The  object  is  placed  at  2  F  in  front,  and  the 

plate  is  placed  at  2  F, 
back  of  the  lens  in  the 
box.  (Figure  113.) 

It  is  used  for  taking 
photographs  of  machinery 
and  parts  of  machinery, 
and  sometimes  of  per- 


FlGURE    112. — AN    ASTIGMATIZED    EYE 

CORRECTED. 


sons. 


146.  The  Projection  Lantern.  —  The  projection  lantern 
(Figure  114)  is  an  application  of  the  converging  lens  with 
the  object  placed  between  F  and  2  F. 


THE   MOTION-PICTURE   MACHINE 


123 


An  arc  light  is  used  to  illuminate  the  object  (0,  Figure 
114),  which  is  usually  a  picture  on  a  glass  plate  called  a 
slide.  In  order  that  more  of  the  light  from  the  arc  may 
strike  the  object,  and  in  order  that  it  may  come  in  parallel 


FIGURE  113.  —  A  LIFE-SIZE  PICTURE  CAMERA. 

rays,  condensing  lenses   (c,  c)   are  placed  between  the  arc 
and  the  object. 

Now,  the  slide  or  object  is  placed  between  F  and  2  F  be- 
tween the  light  and  the  lens,  and  the  image  is  thrown  on  a 
screen  some  distance  in  front,  the  image  appearing  very  large 


Arc 


FIGURE  114. — A  PROJECTION  LANTERN. 


and  inverted.  To  make  the  image  erect,  the  slide  is  placed 
in  the  machine  upside  down. 

147.  The  Motion-picture  Machine.  —  The  motion-picture 
machine  is  merely  a  projection  lantern  with  an  attachment 
for  changing  the  slides  at  the  rate  of  16  or  more  per  second. 

When  images  fall  on  the  retina  of  the  eye  their  effects 
tend  to  linger  ;  that  is,  after  the  image  has  left  the  retina  the 


124 


REFRACTION   AND   LENSES 


FIGURE  115. — A 
DARK  LANTERN. 


nerves  do  not  lose  the  effect  immediately,  and  we  continue 
to  see  the  image  for  about  ^  of  a  second  after  it  is  gone. 

Now,  by  throwing  pictures  upon  a  screen  at  the  rate  of 
16  per  second  the  last  picture  has  not  left  our  mind  before 
the  next  one  has  come.     This  makes  the 
pictures  appear  to  be  continuous. 

Thus  we  see  the  motion  that  takes 
place  if  pictures  are  taken  at  the  rate 
of  16  per  second  and  reproduced  at  that 
rate. 

The  pictures  are  taken  on  a  long  film 
and  are  about  f"  XI"  in  size.  This  film  is  run  off  a  reel, 
through  the  motion-picture  machine,  on  to  another  reel. 

148.  The     Dark 
Lantern.  —  A      good 
example  of  the   con- 
verging lens  with  the 
object    at    F    is   the 
dark  lantern.   (Figure 
115.) 

Here  the  light  is 
placed  at  the  prin- 
cipal focus,  and  after 
passing  through  the 
lens  it  goes  in  a 
parallel  beam. 

149.  The  Magnify- 
ing   Glass.  —  Figure 
116  shows  a  converg- 
ing   lens    used    as    a 

magnifying    glass.  Image 

The  lens  is  held  at  a      FIGURE   1  1 6.  —  A  POCKET  MAGNIFYING  GLASS. 


DIFFUSED  LIGHT 


125 


distance  less  than  F,  and   a  large,  erect,  virtual  image   is 
obtained. 

The  magnifying  glass  is  often  used  as  a  reading-glass.  It 
is  also  used  by  biologists  for  examining  plants  and  small 
insects. 

150.  Diffused  Light.  —  Figure  117  (b)  shows  a  beam  of 
light  falling  on  an  irregular  surface.  Part  of  the  light  is 
absorbed,  but  the  rest 
is  reflected  according 
to  the  law  of  reflection, 
making  the  angle  of 
reflection  equal  to  the 

angle  of  incidence.  FlGURE  1 17. -EXPLAINING  DIFFUSED  LIGHT. 

Since  the  surface  is 

irregular,  the  light   is  reflected  in  every  direction.     These 
reflected  rays  are  called  diffused  light. 


FIGURE  118. — THE  AUTOMOBILE  HEAD-LIGHT  LENS  DIFFUSES 
THE  LIGHT. 

It  is  by  diffused  light  that  we  see  all  bodies  which  are  not 
incandescent,   that  is,   light  giving.     An   object   such   as  a 


126  REFRACTION    AND   LENSES 

perfect  mirror  (a,  Figure  117),  which  reflects  the  light  in 
parallel  rays,  cannot  be  seen.  This  is  illustrated  by  the 
fact  that  a  person  will  sometimes  walk  into  a  mirror  and 
not  know  it  until  he  has  struck  it.  One  looking  into  the 
mirror  does  not  see  the  mirror,  but  only  the  objects  re- 
flected in  it. 


CHAPTER   XI 
ILLUMINATION   AND    CANDLE   POWER 

151.  Intensity  of  Illumination.  —  One  often  desires  to 
speak  of  the  amount  of  light  falling  on  a  surface.  To  ex- 
press this,  the  term  intensity  of  illumination  is  used. 

The  intensity  of  illumination  is  the  light  energy  per  unit 
area. 

To  illustrate  this  definition,  suppose  you  had  a  slice  of 
bread  and  were  to  spread  a  serving  of  butter  upon  it.  The 
butter  would  be  of  a  certain  thickness.  Now,  if  an  equal 
serving  of  butter  were  spread  on  several  slices,  its  thickness 
would  be  much  less.  This  is  true  of  light. 

When  a  certain  amount  of  light  falls  on  a  definite  area 
the  intensity  of  illumination  is  a  certain  amount;  but  if 
the  same  light  were  spread  over  a  larger  area,  the  intensity 
would  be  less. 

Every  one  has  noticed  that  the  greater  the  distance  from 
the  source  of  light,  the  weaker  the  light  becomes.  This  is 
stated  in  the  following  law : 

The  intensity  of  illumination  is  inversely  proportional  to 
the  square  of  the  distance  from  the  source  of  light. 

To  prove  this  law,  suppose  a  cardboard  (a,  Figure  119) 
is  placed  before  a  light  (L),  the  cardboard  having  a  small 
hole  in  it.  A  second  cardboard  (b)  with  a  square  hole,  one 
inch  on  a  side,  cut  in  it  is  placed  one  foot  from  a.  A  third 
cardboard  (c)  is  placed  two  feet  from  a. 

127 


128 


ILLUMINATION    AND   CANDLE   POWER 


Now,  the  light  coming  through  the  square  hole  in  6  falls 
on  a  certain  area  on  c. 

From  the  figure  it  will  be  seen  that  the  side  of  the  illu- 
minated square  on  c  is  twice  the  side  of  the  square  in  b. 


a  b  c 

FIGURE  119.  —  EXPLAINING  LAW  OF  INTENSITY  OF  ILLUMINATION  AS  THE 
DISTANCE  VARIES. 

Thus  the  light  falls  on  an  area  at  c,  which  is  four  times  as 
large  as  on  b ;  etc. 

Thus  the  area  on  which  the  light  falls  is  directly  proportional 
to  the  square  of  the  distance  from  the  source. 

Since  the  intensity  of  illumination  is  inversely  propor- 
tional to  the  area,  it  is  inversely  proportional  to  the  square 
of  the  distance  from  the  object  under  consideration  to  the 
source  of  light. 

This  law  can  be  applied  to  reading.  If  your  book  is 
three  feet  from  the  lamp  the  printed  pages  will  be  illu- 
minated four  times  as  strongly  as  if  it  were  six  feet  away; 
nine  times  as  strongly  as  if  it  were  nine  feet  away;  and 
10,000  times  as  strongly  as  if  it  were  300  feet  away.  This 
shows  you  why  it  is  so  important  to  get  close  to  the  light 
to  get  proper  illumination. 

152.  Candle  Power.  —  We  have  discussed  the  intensity 
of  illumination  of  objects  lighted  by  some  source  other  than 
themselves ;  but  it  is  often  desired  to  express  the  brightness 


MEASUREMENT  OF   CANDLE   POWER 


129 


of  the  source  of  light  itself.  The  unit  used  for  this  is  called 
the  candle  power. 

One  candle  power  is  the  light  given  by  a  standard  candle 
burning  under  specified  conditions. 

The  standard  candle  is  made  of  sperm  oil,  weighs  ^  of 
a  pound,  is  usually  wrapped  in  tinfoil,  and  burns  at  the 
rate  of  120  grains  per  hour. 

It  will  be  seen  immediately  that  the  unit  candle  power  is, 
at  best,  a  poor  unit,  because  no  matter  how  much  care  is 
taken  to  get  the  conditions  the  same,  a  candle  will  never 
give  exactly  the  same  light.  It  is  like  using  a  tape  measure 
made  of  rubber.  Nevertheless,  this  unit  is  still  used  for 
want  of  a  better  one. 

153.  Measurement  of  Candle  Power.  —  In  measuring  the 
candle  power  of  a  source  of  light,  the  light  is  compared  to 
either  a  standard  candle  or  to 
another  light  of  which  the 
candle  power  is  known.  To 
make  this  comparison  the 
photometer  is  used. 

The  photometer  is  a  piece 
of  paper  with  a  grease  spot  on 
it.  This  paper  may  be  either 
placed  in  a  small  black  box 
(Figure  120),  or  may  be  put 
in  a  standard  which  holds  it 
in  position. 

To  compare  two  lights,  the 

photometer  is  held  between  them,  at  such  positions  that 
the  illuminations  on  both  sides  of  the  paper  are  the  same. 
(Figure  121.) 

This  point  can  be  determined,  since  the  grease  spot  will 


FIGURE  120.  —  CROSS  SECTION  OF 
EUNSEN  PHOTOMETER. 


130          ILLUMINATION   AND   CANDLE    POWER 

disappear,  or  look  the  same  shade  on  both  sides,  when  the 
correct  position  is  reached. 

By  measuring  the  distance  (dx)  of  the  unknown  light  ( X} 
to  the  photometer,  and  the  distance  (ds)  from  the  known 


S  X 

FIGURE  121.  —  COMPARING  Two  LIGHTS  BY  USE  OF  PHOTOMETER. 

standard  (S)  to  the  photometer,  the  candle  power  of  X  can 
be  calculated. 


The  candle  power  of  a  few  sources  of  light  are  as  follows  : 

Carbon  Lamp        ......  about  y  c.  p.  per  watt 

Tungsten  Lamp    ......  about  4  c.  p.  per  watt 

Nitrogen  Lamp     ......  about  1  c.  p.  per  watt 

Mercury  Vapor  Lamp    ....  about  1  c.  p.  per  watt 

Arc  Light     ........  about  1  c.  p.  per  watt 

154.  Problems  in  Illumination.  —  The  problem  of  the 
proper  illumination  of  different  kinds  of  buildings,  streets, 
etc.  is  an  important  one.  It  is  one  which  cannot  be  an- 
swered or  solved  in  this  text.  Only  a  few  suggestions  as 
to  its  importance  and  application  can  be  made. 

In  the  home,  care  should  be  taken  to  have  lights  placed 
in  the  proper  positions.  Also,  candle  power  of  lamps  to  be 
used  is  largely  determined  by  the  decorations  of  the  room. 

For  the  kitchen,  two  lamps  are  usually  needed  :  one  above 
the  sink,  and  one  above  the  stove.  Forty-watt  tungsten 
lamps  are,  as  a  rule,  a  good  rating. 


PROBLEMS  IN  ILLUMINATION  131 

A  bedroom  should  have  at  least  a  40-watt  tungsten. 
This  should  be  hung  above  the  dresser  or  dressing  table, 
and  not  from  the  center  of  the  ceiling. 

The  bathroom  should  have  two  lamps,  one  on  each  side 
of  the  mirror.  Twenty-five-watt  tungstens  are  sufficient. 

The  lamps  in  the  living  rooms,  library,  etc.,  cannot  be 
specified,  but  should  be  placed  so  as  to  be  most  convenient 
and  at  the  same  time  bring  out  the  desired  effects  of  the 
decorations. 

It  is  astonishing  what  different  effects  may  be  obtained 
by  different  lightings  of  the  same  piece  of  statuary.  The 
same  is  true  of  paintings. 


CHAPTER   XII 
COLOR 

155.  Dispersion.  —  If  a  ray  of  white  light  be  passed 
through  a  glass  prism  (Figure  122),  it  will  be  refracted  and 
at  the  same  time  will  be  broken  up  into  a  band  of  seven 
colors,  in  the  order  of  violet,  indigo,  blue,  green,  yellow,  orange, 
and  red  (vibgyor  contains  the  initials  of  the  colors  in  the 


FIGURE  122.  —  WHITE  LIGHT  PASSING  THROUGH  A  PRISM. 

regular  order).  This  breaking  up  of  white  light  is  called 
dispersion,  and  the  band  of  seven  colors  is  called  the  solar 
spectrum . 

156.  Cause  of  Different  Colors.  —  At  the  beginning  of 
our  discussion  of  light  we  said  that  light  is  a  wave  motion 
in  the  ether.  Different  wave  lengths  give  differently  colored 
light ;  that  is,  the  color  of  the  light  depends  upon  the  wave 
length,  just  as  the  high  tones  in  sound  have  different  wave 
lengths  from  the  low  tones. 

132 


THE  ACHROMATIC  LENS 


133 


The  violet  rays  are  the  shortest  waves  (about  .000033  cm.) 
which  the  eye  can  see,  while  the  red  rays  are  the  longest 
(about  .000081  cm.),  the  other  colors  falling  in  between, 
in  the  given  order. 

When  a  piece  of  iron  is  heated,  it  first  becomes  red  hot 
and  later  white  hot.  As  more  heat  is  applied,  the  molecules 
vibrate  faster  and  faster,  sending  out  shorter  and  shorter 
wave  lengths  as  well  as  the  longer  ones,  thus  producing  all 
the  colors  of  the  spectrum.  Just  as  white  light  can  be 
broken  up  into  all  these  colors,  so  they  now  combine  and 
make  the  iron  look  white.  Hence  the  term  white  hot. 

This  same  thing  can  be  noticed  in  the  filament  of  an 
electric  lamp  when  it  is  partially  lighted,  then  fully  lighted. 

157.  The  Achromatic  Lens.  —  When  a  lens  is  made  of 
one  piece  of  glass,  it  does  not  refract  all  colors  equally;   in 
other   words,    dispersion    takes 

place.  This  makes  it  impos- 
sible to  get  a  perfect  focus  with 
this  kind  of  lens. 

To  correct  this  defect,  lenses 
are  made  of  crown  and  flint 
glass.  (Figure  123.)  The  dis- 
persive effect  of  one  glass 

counteracts  the  dispersive  effect  of  the  other,  but  the  rays 
are  still  refracted,  thus  producing  a  perfect  focus.  This 
kind  of  lens  is  called  achromatic  —  without  color.  These 
lenses  are  very  expensive  and  are  used  only  in  high-priced 
cameras,  microscopes,  and  other  optical  instruments. 

158.  Transparent,  Translucent,  and  Opaque  Objects.  — 
Objects  are  divided  into  three  classes,  according  to  their 
ability  to  transmit  light. 

Transparent   objects   are   those   which   transmit   light   in 


Whife 


FIGURE  123.  —  AN  ACHROMATIC 
LENS. 


134  COLOR 

parallel  rays ;  and  thus  objects  can  be  seen  in  detail  through 
them. 

Translucent  objects  are  those  which  transmit  light,  but  not 
in  parallel  rays,  so  that  objects  cannot  be  seen  in  detail 
through  them.  Light  after  coming  through  a  translucent 
object  is  diffused. 

Opaque  objects  are  those  which  shut  off  the  light  entirely. 

Air,  clear  plane  glass,  clear  water,  etc.,  are  examples  of 
transparent  objects. 

Snow,  cracked  ice,  frosted  glass,  thin  paper,  etc.,  are 
examples  of  translucent  objects. 

Wood,  iron,  stone,  etc.,  are  examples  of  opaque  objects. 

159.  Color  of  Opaque  Objects.  —  No  object,  unless  it  is 
self-illuminated,  has  color.     It  gets  its  color  from  the  light 
that  falls  on  it. 

The  light  that  falls  on  it  is  either  absorbed  or  reflected, 
the  object  taking  on  the  color  of  the  light  that  it  reflects. 
Thus  a  red  dress  is  not  red  at  all,  but  merely  absorbs  all 
colors  that  fall  on  it  except  red,  which  it  reflects,  thus  giving 
it  the  apparent  red  color. 

This  same  red  dress  in  a  perfectly  dark  room  would  be 
black.  It  would  also  be  black,  or  purplish  (depending  upon 
the  shade  of  red),  if  held  in  the  light  of  a  sodium  flame, 
because  this  light  contains  only  yellow,  and  so  there  would 
be  no  red  to  be  reflected. 

160.  Dyes.  —  A  dye  is  a  substance  which  may  be  made 
to  stick  between  the  fibers  of  another  object  and  thus  give 
the  object  an  apparent  color  by  reflecting  that  colored  light. 

Cloth  is  usually  dyed  by  placing  it  in  a  liquid  containing 
certain  substances  which  enter  the  cloth  and  stick  between 
the  fibers  after  the  dye  has  dried.  If  it  is  a  good  dye,  it  is 
of  such  a  nature  that  these  particles  cannot  be  washed  out, 


APPLICATION  OF  COLORED  OBJECTS.     135 

causing  the  cloth  to  fade.     A  good  dye  should  also  be  un- 
affected by  sunlight. 

When  a  cloth  fades,  the  small  particles  are  either  washed 
out  or  are  so  changed  chemically  that  they  will  not  reflect 
the  desired  color. 

161.  Paints.  —  Paints   are   different   from   dyes   in   that 
they  are  colored  pigments  which  are  spread  over  the -surf ace 
of  an  object,  instead  of  going  in  between  the  fibers.     The 
color  of  the  paint  is  determined  by  the  colored  light  which 
the  pigments  reflect. 

162.  Color  of  Transparent  and   Translucent  Objects.  — 
Transparent  and  translucent  objects  get  their  color  from 
the  light  which  they  transmit.     A  green  glass  is  green  be- 
cause it  absorbs  all  other  colors  and  transmits  the  green. 
Objects  viewed  through  green  glass  appear  green  because 
that  is  the  only  kind  of  light  that  gets  through. 

Colored  glass  is  made  either  by  putting  the  coloring 
material  in  the  glass  when  it  is  manufactured,  or  else  by 
covering  the  glass  with  a  film  of  gelatin  containing  the 
coloring-matter. 

163.  Application  of  Colored  Objects.  —  From  the  preced- 
ing topics  it  is  seen  that  the  color  of  an  object  depends  upon 
two  things :  the  kind  of  light  falling  on  it,  and  the  color  which 
it  reflects  or  transmits. 

The  knowledge  of  this  f act  is  applicable  in  the  selection 
of  dress  goods  and  in  the  illumination  of  pictures  and  other 
decorations. 

In  selecting  dress  goods,  the  selection  should  be  made  in 
the  same  kind  of  light  as  that  in  which  the  dress  is  to  be 
worn.  For  example,  if  a  piece  of  goods  is  selected  in  arti- 
ficial light,  it  should  be  worn  in  the  same  kind  of  artificial 
light,  for  it  may  be  of  an  entirely  different  color  when  viewed 


136  COLOR 

in  daylight.  As  an  exaggerated  example,  a  bright  red  piece 
of  cloth  in  daylight  would  appear  dark  purple  or  black  in 
the  light  of  a  mercury  vapor  lamp.  This  is  because  there 
is  no  red  light  given  off  by  the  mercury  lamp,  and  conse- 
quently the  material  has  no  red  to  reflect. 

In  the  same  way  a  blue  piece  of  goods  in  daylight  looks 
black  under  a  carbon  lamp,  since  the  carbon  lamp  gives  off 
very  little  blue  light. 

The  same  application  can  be  made  in  illuminating  pic- 
tures, wall  paper,  draperies,  etc.  These  decorations  will 
take  on  an  entirely  different  color  when  placed  under  differ- 
ent colored  lights. 

A  lamp  has  recently  been  put  on  the  market,  called  the 
"  day-light  lamp."  It  is  given  this  name  because  the  rays 
sent  out  by  it  contain  the  same  colors,  and  in  the  same 
proportion,  as  are  found  in  sunlight.  Most  large  stores  now 
have  these  lamps,  so  that  goods  selected  in  this  light  will 
have  the  same  color  in  sunlight. 

164.  The  Three  Primary  Colors.  —  It  was  found  that  by 
passing  white  sunlight  through  a  prism  it  could  be  dispersed 
into  seven  colors. 

Each  of  these  colors  is  elementary  ;  that  is,  it  cannot  be 
broken  up  into  parts  or  other  colors.  This  would  lead  us 
to  believe  that  to  get  white  light  we  must  mix  these  seven 
colors,  and  this  is  partially  true. 

A  mixture  of  these  seven  colors  in  the  right  proportions 
will  give  white  light,  but  white  light  can  also  be  obtained 
by  the  mixture  of  three  elementary  colors  :  red,  green,  and 
violet.  More  than  that,  any  color  whatsoever  can  be  ob- 
tained by  the  correct  proportions  of  these  three  colors. 

For  this  reason  the  three  colors  red,  green,  and  violet  are 
called  the  primary  colors  of  light. 


MIXING   COLORED  LIGHTS  137 

165.  How  We  See  Color.  —  Referring  back  to  the  topic 
on  "  The  Eye  "   (§   142),  it  will  be  found  that  the  retina, 
the  inner  lining  of  the  back  of  the  eye,  is  composed  of 
countless    numbers    of  nerve-endings    or    cells,    that    these 
cells  are  divided  into  three  classes,  but  are  all  intermingled, 
so  that  even  the  smallest  spot  on  the  retina  has  all  three 
kinds  of  cells. 

One  of  these  classes  of  cells  is  affected  by  red  light,  and  red 
only  ;  another  is  affected  by  green  light,  and  green  only  ; 
while  the  third  class  is  affected  by  violet  light,  and  violet 
only. 

Now,  when  an  image  falls  on  the  retina,  these  cells  are 
affected  by  the  light  that  strikes  them.  Where  only  red 
light  falls,  only  those  corresponding  nerve  cells  are  affected ; 
the  same  for  green  ;  and  the  same  for  violet. 

If  a  light  such  as  yellow,  which  is  composed  of  both  red 
and  green,  falls  on  a  spot  on  the  retina,  both  those  corre- 
sponding kinds  of  cells  are  affected. 

When  these  cells  are  affected,  impulses  are  sent  to  cor- 
responding nerve  cells  in  the  brain,  and  we  become  con- 
scious of  those  certain  kinds  of  light  falling  on  their  respective 
positions  on  the  retina.  Thus  we  know  the  shape  of  the  ob- 
ject and  also  its  color. 

166.  Mixing  Colored  Lights.  —  It  has  been  noted  that 
lights   of   different   colors   may   be   mixed.     When   this   is 
done,  the  result  is  the  combined  effects  of  all    he  lights  each 
taken  separately.     This  is  called  the  additive  method. 

Thus,  when  the  correct  proportions  of  red  light  and  green 
light  are  superimposed,  the  result  is  the  sum  of  the  red  and 
green  effects,  which  gives  a  yellow.  Likewise,  any  color 
whatsoever  may  be  produced  by  adding  the  proper  portions 
of  the  three  primary  colors. 


138 


COLOR 


The  above  statements  can  be  experimentally  illustrated 
by  the  use  of  colored  disks  on  a  turning  table.     (Figure  124.) 
By  placing  these  disks  on  the  spindle, 
one  over  the  other,  in  such  a  manner 
that  a  certain  portion  of  each  disk  is 
visible,  and  then  by  turning  the  disks 
at  a  rapid  rate,  an  apparent  mixture  of 
these  colors   is  attained.     The  mixing 

is  done  on  the  same  principle  as   the 
FIGURE  124.  —  COLORED          .  .          .  /e  .. 

DlSKS  moving-picture  (§  147),  each  color  effect 

being  superimposed  upon  the  retina  of 
the  eye  before  the  other  color  effects  disappear. 

167.  Tints  and  Shades.  —  A  tint   of  a  certain  color  is 
produced  by  adding  that  color  to  white.     In  the  same  way 
shades  of  a  color  are  produced  by  mixing  that  color  with 
black. 

168.  Colored  Pigments.  —  Colored  pigments  are  used  in 
paints  and  dyes,  and  are  small  particles  of  matter  of  such  a 
nature  that  they  reflect  certain  colors. 

169.  Mixing  Pigments. 
''• —  Mixing     pigments    to 
produce    color    is    called 
the  subtr active  method.     It 
is  called  subtractive  be- 
cause   the   color    that   is 
given  out  after  mixing  the 
pigments  is  that  which  is 
left    after    the    pigments 
have  absorbed  their  char- 
acteristic   colors.      Thus 

Figure  125  illustrates  the      F,OURE  125._ADDING  RED,  YELLOW, 
adding  of  red  and  yellow,  AND  VIOLET  LIGHTS. 


MIXING  PIGMENTS 


139 


White 


Light 


Light  Gray 


Light  Graj 


— Neutral  Gray 


-Dark  Gra> 


Dark 


Dark  Gray 


FIGURE  126. — -MIXING  Six 
DIFFERENT  COLORED  PIG- 
MENTS. 


yellow  and  violet,  violet  and  red,  and  red,  yellow,  and  violet. 

It  will  be  seen  that  the  resulting  colors  are,  respectively, 

orange,  green,  purple,  and  black. 
The    three    kinds    of    pigments, 

red,  yellow,  and  violet,  are  called 

primary,  because   by  adding  them 

in    the    right   proportion    black    is 

obtained. 

Each  of  the 
three  kinds  of 
pigments  absorbs 
certain  colors, 
giving  back  only 
its  characteristic 

color.  When  the  three  kinds  are  mixed 
together,  no  color  is  given  back,  for 
what  one  gives  back  the  others  absorb. 
This  produces  the  absence  of  color,  or 
black. 

Figure  126  is  a  diagram  illustrating  the 
mixing  of  six  kinds  of  pigments,  and  the 
resulting  effects.  Thus  a  mixture  of  red 
and  orange  gives  a  red-orange  ;  a  mix- 
ture of  orange  and  yellow  gives  an 
orange-yellow,  etc. 

Opposite  colors,  such  as  red  and  green, 
orange  and  blue*  yellow  and  violet,  are 
called  complementary  colors,  because  if 
the  one  is  taken  from  white  the  other  is 
the  result.  For  example,  if  red  is  taken 
from  white,  green  is  the  result,  etc. 
Figure  127  is  a  diagram  showing  how 


Black 

FIGURE  127.  —  DIF- 
FERENT SHADES  OF 
GRAY. 


140  COLOR 

to  obtain  different  shades  of  gray.  Half  white  and  half 
black  give  what  is  called  neutral  gray.  Three-fourths  black 
and  one-fourth  white  give  a  dark  gray.  Three-fourths  white 
and  one-fourth  black  give  a  light  gray.  Greater  quantities 
of  black  than  three-fourths  give  a  dark  dark-gray.  Greater 
quantities  of  white  than  three-fourths  give  a  light  light-gray, 
etc.  Thus  any  shade  from  white  to  black  may  be  obtained 
by  a  mixture  of  the  proper  proportions. 

170.  Limitations  of  Color  Nomenclature.  —  We  use  the 
terms  red,  blue,  green,  pink,  pea-green,  sky-blue,  etc.,  very 
freely,  as  if  they  were  definite  in  meaning.     The  fact  of 
the  matter  is,  they  are  very  indefinite. 

For  example,  could  you  tell  exactly  what  color  to  get  if 
you  were  sent  to  buy  sky-blue  or  pea-green  silk?  The 
trouble  is,  our  terms  are  not.  definite,  but  cover  a  wide 
range  of  color.  We  still  use  these  indefinite  terms  for 
want  of  better  substitutes. 

171.  Harmony  of  Color.  —  In  music  certain  tones  sound 
pleasing    when    given    together.     The    law    governing    the 
combining  of  these  tones  is  called  harmony.     In  the  case 
of  colors  it  is  just  as  true  that  certain  combinations  of  color 
are  pleasing,  while  others  are  not.     We  speak  of  this  as  the 
harmony  of  color. 

So  far  there  are  few  set  rules  or  laws  governing  these 
combinations,  since  they  are  left  to  the  taste  of  the  in- 
dividual. What  looks  well  to  one  individual  may  be  almost 
shocking  to  another. 

It  is  true,  however,  that  the  following  simple  rule  can  be 
followed,  and  that,  in  general,  it  will  give  a  pleasing  com- 
bination. All  colors  harmonize  with  black  and  with  white. 

172.  Half-tone  Picture  Printing.  —  In  half-tone    picture 
printing  a  negative  is  obtained  from  either  the  object  itself 


HALF-TONE  PICTURE   PRINTING 


141 


or  from  a  photograph,  in  exactly  the  same  manner  as  in 
photography. 

Instead  of  printing  on  a  sensitized  paper  as  in  the  case 
of  a  photograph,  the  negative  is  placed  over  a  sensitized 
plate  of  copper  or  other  metal,  and  the  picture  is  printed  on 
this.. 

The  copper  plate  is  made  sensitive  by  a  covering  of  gelatin 
sensitive  to  light,  just  as  in  the  case  of  the  paper. 

Before  the  printing  on  the  metal  plate  is  begun,  two  glass 
screens  (a  and  6,  Figure  128)  are  placed,  one  over  the  other, 
between  the  negative  and 
the  plate.    These  screens 
are    usually    ruled    with 
from  100  to  150  parallel 
lines   to   the    inch,   and, 
when    placed    over    one 
another  (c),  the  lines  of 

one  are  perpendicular  to  the  lines  of  the  other;    the  lines 
being  scratches  which  shut  off  light. 

In  printing,  the  light  shines  through  the  light  part  of  the 
negative,  turning  the  sensitive  gelatin  on  the  metal  plate 
black,  and  making  it  insoluble.  The  rest  of  the  gelatin 
is  unaffected,  and  when  "  washed  "  dissolves,  leaving  the 
black,  insoluble  part  on  the  plate.  The  lines  of  the  screens 
appear  as  clean  lines  on  the  plate. 

This  metal  plate  is  then  subjected  to  an  acid  bath  which 
etches,  or  eats  away  the  unprotected  part  of  the  plate,  leav- 
ing the  part  covered  with  gelatin  "  raised  "  or  level  with 
the  original  surface. 

After  scraping  off  this  gelatin  the  plate  may  be  inked 
and  used  for  actual  printing  of  pictures  in  books,  magazines, 
or  newspapers. 


a  b  c 

FIGURE  128.  —  LIGHT  SCREENS. 


142 


COLOR 


Since  most  printing  is  done  from  rolls,  the  impression 
may  be  transferred  from  the  metal  sheet  to  the  rolls  by  the 
electrotype  method.  (§  280.) 

By  referring  to  Figure  129  it  can  be  seen  why  the  metal 
plate  will  produce  a  picture  which  is  the  exact  likeness  of 
the  object. 

The  light  part  of  the  negative  represents  the  dark  part 
of  the  object.  The  raised  part  of  the  metal  plate  represents 
the  light  part  of  the  negative  or  the  dark  part  of  the  object, 


Object  Negative  Plate 

FIGURE  129.  —  DIAGRAM  SHOWING  OBJECT,  NEGATIVE,  AND  PLATE  IN 
HALF-TONE  PICTURE  PRINTING. 

the  lines  of  the  two  screens  appearing  as  depressed  parts  on 
the  metal  plate. 

Now,  when  the  metal  plate  is  inked  and  a  picture  is 
printed  with  it,  the  raised  portion  is  the  only  part  that 
prints,  thus  reproducing  the  dark  parts  of  the  object  in  ink. 
The  lines  are  to  keep  the  ink  from  "  running."  They  do 
not  show,  except  upon  close  examination,  in  the  printed 
picture. 

173.  The  Three-color  Printing  Process.  —  The  half-tone 
picture  printing  process,  discussed  in  §  172,  gives  a  picture 
in  light  and  shadow  only.  This  process  has  been  enlarged 
upon,  and  now  pictures  in  actual  colors  can  be  printed  by 
what  is  called  the  "  three-color  process."  This  process  is 


THE   THREE-COLOR  PRINTING   PROCESS         143 

used  to  print  the  colored  cover  designs  and  colored  advertise- 
ments used  so  much  in  the  better  magazines. 

In  this  process  three  negatives  are  taken  through  three 
separate  light  filters.  The  three  filters  consist  of  three  plates 
of  glass  stained  violet,  blue-green,  and  orange,  respectively. 

These  filters  are  placed  in  front  of  the  camera,  one  at  a 
time,  when  the  three  negatives  are  taken.  The  negatives 
are  developed  and  printed  on  three  separate  metal  plates, 
as  in  the  half-tone  process. 

These  plates,  or  their  reproduced  rolls,  are  then  inked,  — 
the  one  corresponding  to  the  violet  filter  with  yellow  ink,  the 
one  corresponding  to  the  blue-green  filter  with  red-orange 
ink,  and  the  one  corresponding  to  the  orange  filter  with  blue 
ink.  Then  all  three  are  successively  printed  on  the  same 
sheet  of  white  paper.  The  result  is  a  picture  of  the  object 
in  actual  colors,  or  at  least  approximating  the  actual  colors, 
the  degree  of  accuracy  in  colors  depending  on,  the  trueness 
of  the  colors  of  the  filters  and  inks  used. 

The  reasons  why  this  process  gives  the  actual  colors  are 
as  follows : 

In  the  first  place,  the  negative  taken  with  a  violet  filter 
has  dark  spots  only  where  the  violet  light  strikes,  and  so  the 
corresponding  metal  plate  has  depressed  spots  representing 
the  violet  of  the  object. 

Likewise,  the  metal  plate  corresponding  to  the  blue-green 
filter  has  depressed  spots  representing  the  blue-green  of  the 
object,  and  the  metal  plate  corresponding  to  the  orange  filter 
has  depressed  spots  representing  the  orange  of  the  object. 

Now,  the  three  colors,  violet,  blue-green,  and  orange,  con- 
tain all  the  colors  of  white  light,  and  so  the  depressions  in 
the  three  metal  plates  represent  all  the  actual  colors  of  the 
object. 


144  COLOR 

The  plate  corresponding  to  violet  in  the  object,  covers  all 
the  rest  of  the  white  paper  with  yellow,  the  complementary 
pigment  of  violet.  Likewise,  the  plate  corresponding  to 
blue-green  in  the  object  covers  all  the  rest  of  the  white  paper 
with  red-orange,  and  the  plate  corresponding  to  orange  in 
the  object  covers  all  the  rest  -of  the 

Cohr  niter  /„*  J  . 

white  paper  with  blue.  The  spots 
with  yellow  ink  reflect  all  colors  but 
violet,  or,  in  other  words,  blue-green 
and  orange.  (Figure  130.)  Also, 
the  spots  with  red-orange  ink  reflect 
all  colors  but  blue-green,  or  in  other 
words  violet  and  orange. 
FIGURE  1 30.  -  DIAGRAM.  Therefore  a  spot  covered  by 

yellow  and    red-orange  inks   reflects 

only  orange.     Also  a  spot  covered  by  yellow  and  blue  inks 

reflects  only  blue-green,  and  a  spot  covered  by  red-orange  and 

blue  inks  reflects  only  violet. 

This  makes  the  printed  picture  reflect  the  actual  colors  of 

the  object  in  the  correct  positions  and  amounts. 

Review  Problems 

1.  What  is  the  theory  of  the  nature  of  light  ? 

2.  When  is  a  body  luminous  ? 

3.  Why  can  you  see  a  body  which  is  not  luminous? 

4.  What  is  the  velocity  of  light  ? 

5.  Explain  Roemer's  method  for  determining  the  velocity  of  light. 

6.  Give  two  comparisons  which  will   show  the  magnitude  of  the 
velocity  of  light. 

7.  Give  the  law  cf  reflection. 

8.  Does  your  right  hand  appear  to  be  the  right  hand  of  your  image 
in  a  plane  mirror? 

9.  Construct  the  image  in  a  plane  mirror.     Describe  the  image. 


REVIEW  PROBLEMS  145 

10.  Construct  the  image  in  a  concave  mirror,  (a)  when  object  is 
beyond  center  of  curvature,  (6)  when  object  is  at  center  of  curvature, 

(c)  when  object  is  between  center  of  curvature  and  principal  focus, 

(d)  when  object  is  at  principal  focus,  (e)  when  object  is  between  prin- 
cipal focus  and  mirror. 

11.  Give  two  uses  of  the  convex  mirror. 

12.  Give  two  uses  of  the  concave  mirror. 

13.  Explain  why  refraction  takes  place. 

14.  Give  five  applications  of  refraction. 

15.  Construct  the  image  in  the  five  different  settings  of  the  convex 
lens. 

16.  Give  an  application  of  each  of  the  five  settings  of  the  convex 
lens. 

17.  Explain  how  a  photograph  is  made. 

18.  What  is  diffused  light? 

19.  What  produces  color  in  a  light? 

20.  Explain  why  an  opaque  object  has  a  certain  color. 

21.  Explain  why  a  stained  glass  has  a  certain  color. 

22.  Why  can  you  not  rely  on  colors  chosen  by  artificial  light  ? 

23.  What   application  has   color   to   the   decorating   and   lighting 
of  a  home? 

24.  Explain  why  shadows  play  an  important  part  in  the  proper 
illumination  of  a  room. 

25.  How  are  half-tones  made  ? 

26.  What  is  a  tint?     What  is  a  shade ? 

27.  What  is  meant  by  the  "  additive  method  "  ? 

28.  What  is  meant  by  the  "  subtractive  method  "  ? 

29.  What  is  the  difference  between  a  dye  and  a  paint  ? 

30.  What  causes  a  colored  piece  of  goods  to  "  fade  "? 


CHAPTER   XIII 
MAGNETISM 

174.  Properties  of  Magnetism.  —  We  do  not  know  just 
what  magnetism  is,  but  we  do  know  many  things  about  it. 
For  centuries  people  have  known  of  a  peculiar  kind  of  ore 
called   "  lodestone,"  which  has  the  property  of  attracting 
iron.     The  "  lodestone  "  is  said  to  have  magnetism,  and  the 
best  definition  we  have  is :   Magnetism  is  the  property  some 
objects  have  of  attracting  iron.     An  object  which  has  mag- 
netism is  said  to  be  a  magnet. 

175.  Poles  of  a  Magnet.  —  If  a  magnet  be  thrust  into  a 
box  of  iron  filings,  the  filings  will  cling  to  the  ends  of  the 
magnet,  and  will  appear  to  be  attracted  to  one  point  near 
each  end.     This  point  is  called  the  pole  of  the  magnet,  and 
is  located  inside  the  iron  some  distance  from  the  end.     The 
pole  of  a  magnet  is  the  point  at  which  all  the  force  of  attraction 
is  centered. 

A  magnet  has  two  poles,  one  near  each  end,  called  north 
(N)  and  south  (S).  It  is  unfortunate  that  they  were  named 
"  north  "  and  "  south/'  for  we  are  apt  to  confuse  these 
terms  with  direction.  A  magnet  may  be  placed  in  any 
position,  and  yet  its  poles  remain  the  same,  regardless  of 
direction.  For  example,  a  magnet  may  be  placed  in  an 
east  and  west  position,  and  yet  its  poles  are  called  N  and  S. 
A  magnet  may  be  easily  placed  so  that  its  N-pole  is  on  the 
south  end  (direction)  of  the  magnet. 

146 


FIELD  OF  A   MAGNET  147 

176.  Law  of  Attraction  and  Repulsion.  —  If  a  magnet  is 
suspended  at  its  middle  by  a  cord,  or  balanced  on  a  pivot, 
and  another  magnet  is  brought  near  it,  the  end  of  the  first 
magnet  is  either  attracted  or  repelled  by  the  other  magnet. 

If  the  N-pole  of  one  comes  near  the  S-pole  of  the  other, 
they  are  attracted,  and  if  free,  will  swing  together.  But  if 
the  S-pole  of  one  magnet  comes  near  the  S-pole  of  the  other, 
they  are  repelled,  and  if  free  will  swing  apart.  Thus  we 
have  this  law :  Unlike  poles  attract  and  like  poles  repel. 

177.  The  Earth  a  Magnet.  —  The  earth  itself  is  a  huge 
magnet,  one  of  its  magnetic  poles  being  about  1000  miles 
from  the  geographical  north  pole,  while  the  other  magnetic 
pole  is  at  a  similar  distance  from  the  geographical  south  pole. 

A  magnet  suspended  so  that  it  is  free  to  swing  in  a  hori- 
zontal plane  will  come  to  rest  in  a  north  and  south  position. 
This  is  due  to  the  magnetic  attraction  of  the  earth.  The 
pole  that  swings  towards  the  north  is  called  "  N-pole," 
while  the  one  that  swings  towards  the  south  is  called  "  S- 
pole."  At  the  time  the  poles  were  named,  people  did  not 
know  that  magnets  would  ever  be  used  for  anything  except 
to  tell  direction,  and  the  names  "  N  "  and  "  $  "  seemed 
appropriate. 

But  now  the  names  are  confusing.  A  N-pole  is  the  pole 
that  points  north  when  the  magnet  is  free  to  swing,  but  by 
the  "  law  of  attraction  "  unlike  poles  attract ;  therefore  the 
magnetic  pole  near  the  north  geographical  pole  is  really  a 
"  S"  magnetic  pole.  Likewise  the  "  N  "  magnetic  pole  of 
the  earth  is  in  the  south. 

178.  Field  of  a  Magnet.  —  We  have  seen  that  a  magnet 
will  attract  iron  filings  even  when  they  are  not  touching  it. 
What  is  it  that  harnesses  the  iron  filings  to  the  magnet, 
since  we  cannot  see,  or  feel,  anything  between  them? 


148 


MAGNETISM 


Evidently  there  is  some  force  in  the  space  about  the  mag- 
net. This  space  is  called  the  "  magnetic  field,"  and  is  said 
to  be  filled  with  "  lines  of  force." 


FIGURE  131.  —  FIELD  ABOUT  A  BAR  MAGNET. 


Just  what  these  lines  of  force  are  no  one  is  able  to  explain  ; 
and  for  want  of  a  better  name  they  are  said  to  be  strains  in 
the  ether. 

If  a  piece  of  paper  is  placed  over  a  bar  magnet  and  iron 
filings  are  sifted  on  it,  the  filings  will  arrange  themselves  in 
lines  as  shown  in  Figure  131. 


FIGURE  132.  —  ARRANGEMENT  OF  MOLE- 
CULES IN  A  PIECE  OF  IRON  NOT  MAG- 
NETIZED. 


FIGURE  1 33.  —  DIAGRAM 
OF  BALANCED  FORCES 
IN  A  PIECE  OF  IRON 
NOT  MAGNETIZED. 


THEORY  OF  MAGNETISM 


149 


179.   Properties  of  Lines  of  Force.  —  Whatever  the  lines 
of  force  are,  they  have  three  known  properties : 


FIGURE    134.  —  ARRANGEMENT   OF    MOLE- 
CULES IN  A  MAGNETIZED  PIECE  OF  IRON. 


FIGURE  135.  —  UNBAL- 
ANCED FORCES  IN  A  MAG- 
NETIZED PIECE  OF  IRON. 


1.   They  have  direction  and  always  come  out  of  a  N-pole 
and  go  in  at  a  S-pole,  completing  a  loop  inside  the  magnet. 


FIGURE  136. —  How  TO  MAGNETIZE  A  PIECE  OF  IRON. 

2,  They  have  a  tendency  to  contract,  like  rubber  bands, 
and  will  contract  until  they  are  zero  in  length. 

3.  They  repel  one  another  laterally. 

180.   Theory  of  Magnetism.  —  Some  substances  are  said 
to  be  magnetic,  while  others  are  non-magnetic.     Magnetic 


FIGURE  137. —  FIELD  BETWEEN  Two  UNLIKE  POLES. 

substances  are  substances  whose  molecules  have  N-  and  S- 
poles,  while  non-magnetic  substances  are  those  whose  mole- 
cules do  not  have  N-  and  S-poles. 


150 


MAGNETISM 


Iron  is  the  most  magnetic  substance,  while  cobalt  and 
nickel  are  only  slightly  magnetic.  Most  substances,  such  as 
wood,  glass,  copper,  brass,  etc.,  are  non-magnetic. 


FIGURE  138.  —  FIELD  BETWEEN  Two  LIKE  POLES. 

The  fact  that  iron  is  magnetic  does  not  necessarily  mean 
that  a  piece  of  it  is  a  magnet.     It  must  first  be  magnetized. 

181.  Difference  between  a  Magnetized  Piece  of  Iron  and 

One  Not  Magnetized.  - 
In  a  piece  of  iron  that  is 
not  magnetized  the  mole- 
cules have  their  N-poles 
and  S-poles  pointing  in 
various  directions  (Figure 
132),  and  the  effect  of 
some  molecules  neutral- 
izes the  effect  of  others. 
It  is  like  several  boys 
pulling  in  all  directions 
upon  a  post.  (Figure 
133.)  The  pull  is  bal- 
anced and  there  is  no 


F.GURE    139.-F.ELD   ABOUT  A    HORSE- 

SHOE  MAONET. 


°" 


But  in  a  piece  of  iron 


HOW   TO  MAGNETIZE  A   PIECE  OF  IRON        151 


which  is  magnetized,  the  molecules  are  all  in  order;  so  that 
all  the  S-poles  point  to  one  end,  and  all  the  N-poles  to  the 
other.  (Figure  134.) 

In  this  case  the  effect  of  each  molecule  helps  the  effect  of 
every  other,  and  one  end  of  the  bar  becomes  a  N-pole  and 
the  other  end  the  S-pole.  To 
illustrate  this  as  before,  all  the 
boys  pull  in  the  same  direction. 
(Figure  135.) 


FIGURE  140. -FIELD  ABOUT  A 
HORSESHOE  MAGNET  HAVING  A 
BAR  OF  SOFT  IRON  IN  FRONT 
OF  POLES. 

182.    How  to  Magnet- 
ize a  Piece  of  Iron.  — 

To  magnetize  a  piece  of 
iron,  place  it  in  a  mag- 
netic field  so  that  the 
lines  of  force  run  through 
the  iron.  This  lines  the 

molecules  up  as  in  Figure  136,  magnetizing  the  iron. 

If  it  is  a  piece  of  tempered  steel  that  has  been  magnetized, 

the  molecules  will  keep  their  positions,  and  the  steel  will  hold 


FIGURE  141.  —  FIELD  ABOUT  A  HORSE- 
SHOE MAGNET  HAVING  A  DISK  OF  SOFT 
IRON  IN  FRONT  OF  POLES. 


152  MAGNETISM 

its  magnetism,  because  the  molecules  cannot  fall  back  out  of 
line.  This  is,  then,  a  permanent  magnet. 

If  the  piece  of  iron  is  soft  and  not  tempered,  the  molecules 
become  disarranged  as  soon  as  the  magnetic  field  is  removed  ; 
and  it  loses  its  magnetism.  This  is  a  temporary  magnet. 

183.  Characteristic  Fields.  —  The  following  drawings 
show  the  direction  of  the  lines  of  force  in  several  cases. 
(Figures  137,  138,  139,  140,  141.) 


CHAPTER   XIV 


ELECTRICITY 

184.  Relation  of  Electricity  to  Magnetism.  —  Before 
studying  the  subject  of  electricity  we  spent  some  time  on 
magnetism,  because  magnetism  and  electricity  are  very 
closely  related.  We  shall  now  find  how  necessary  magnetism 
is  to  the  production  of  electricity. 

The  question  just  .what  electricity  is,  has  never  been  satis- 
factorily answered.  The  latest  theory  is  that  it  is  some  kind 
of  strain  in  the  ether,  and  that  the  strain  will  move  along 
a  wire,  producing  a  current  of  electricity. 

Anything  which  will  transmit  elec- 
tricity from  one  place  to  another  is 
called  a  conductor. 

485.  Generation  of  Electrical  Pres- 
sure. —  It  has  been  found  that  if  a 
conductor  is  moved  in  a  magnetic 
field  so  that  it  cuts  the  lines  of  force 
electrical  pressure  is  produced,  or  is 
said  to  be  generated. 

In  Figure  142  we  have  a  permanent 
magnet  with  the  lines  of  force  shown 

coming  out  of  the  N-pole.  A  copper  wire,  or  rod,  is  held 
in  this  magnetic  field  and  moved  across  the  lines  of  force. 
This  generates  electrical  pressure  in  the  conductor. 

153 


FIGURE   142.  —  GENERAT- 
ING ELECTRICAL  PRESSURE. 


154  ELECTRICITY 

If  a  complete  circuit  is  made  from  one  end  of  the  bar  to 
the  other,  a  current  of  electricity  will  flow. 

The  thing  that  produces  the  pressure  is  cutting  lines  of  force 
with  a  conductor.  This,  then,  is  one  of  the  fundamental 
principles  to  learn  about  electricity.  Whenever  lines  of  force 
are  cut  by  a  conductor,  electrical  pressure  is  generated. 

186.  Nature  of  Electrical  Pressure.  —  But  just  what  is 
electrical  pressure?     Since  electricity  is  an  invisible  some- 
thing and  yet  is  analogous  to  the  flow  of  water,  we  can  best 
get  a  conception  of  it  by  comparing  it  to  the  flow  of  water. 

In  the  case  of  water,  we  say  there  is  a  pressure  of  so  many 
pounds  per  square  inch.  Pressure  is  the  thing  that  makes 
the  water  flow  when  the  stop-cock  is  turned  on.  The  pres- 
sure is  there  whether  the  cock  is  turned  on  or  not,  and  when- 
ever the  water  has  a  chance  to  flow,  the  pressure  forces  it  to 
do  so. 

Electrical  pressure  is  similar.  It  is  that  which  makes  the 
electrical  current  flow.  There  may  be  an  electrical  pressure, 
and  yet  no  current  (if  the  circuit  is  not  closed) ;  but  if  there 
is  a  possibility  for  the  current  to  flow  (as  when  the  circuit 
is  closed)  the  pressure  will  make  it  do  so. 

The  amount  of  electrical  pressure  depends  upon  the  rate  of 
cutting  lines  of  force  ;  or,  we  could  say,  upon  the  number  of 
lines  of  force  cut  per  second. 

The  direction  of  the  pressure  depends  upon  the  direction 
in  which  the  lines  of  force  are  cut. 

187.  Electrical  Current.  —  The  electrical  current  may  be 
compared  to  the  current  of  water  in  a  pipe.     We  say  the 
current  is  large  or  small  according  to  the  amount  of  water  it 
will  deliver  in  a  certain  time.     Similarly  with  electricity, 
the  current  is  the  flow  of  the  electricity,  and  is  measured  by  the 
amount  of  electricity  it  will  deliver  per  second. 


THE  SIMPLE  GENERATOR 


155 


The  size  of  the  current  depends  upon  the  pressure  forcing 
it  to  flow,  and  upon  the  resistance  offered  to  it  by  the  con- 
ductor. 

188.  Resistance.  —  If  the  water  pipe  in  the  above  case 
were  small,  it  would  be  difficult  for  the  water  to  get  through. 
In  other  words,  the  pipe  would  offer  a  resistance  to  the  flow 
of  the  water  current.     The  same  thing  takes  place  in  a  wire. 
The  resistance  is  that  ivhich  tends  to  hold  the  current  back. 

There  are  four  principal  things  which  affect  the  resistance 
of  a  conductor :  (1)  size,  (2)  length,  (3)  kind  of  material, 
(4)  temperature. 

The  larger  the  wire,  the  smaller  the  resistance.  The 
longer  the  wire,  the  greater  the  resistance.  Some  kinds  of 
material  have  more  resistance  than  others.  For  instance, 
copper  has  less  resistance  than  iron. 

Materials  which  have  a  low  resistance  are  said  to  be  good 
conductors.  Copper,  silver,  platinum,  and,  in  fact,  nearly 
all  the  metals  are  good  conductors.  Those  materials  which 
have  an  exceptionally  high  resistance  are  called  insulators, 
such  as  air,  wood,  glass,  mica,  rubber,  asbestos,  etc. 

The  temperature  affects  different  materials  differently. 
With  some,  it  increases  the 
resistance ;  and  with  others 
it  decreases  it.  A  carbon 
lamp  has  less  resistance 
when  hot  than  when  cold, 
but  a  tungsten  lamp  has 
more  resistance  when  hot. 

189.  The  Simple  Gener-    FIOURE  ^  _A  ^  GENERATOR 
ator.  —  Figure  143  shows  a 

loop  of  wire  revolving  in  a  magnetic  field.     The  magnetic 
field  is  produced  by  the  permanent  magnets  N  and  S.     The 


,        ?       r 


3 
3 

^ 

e 

i 

E 

y/fflffitf///0, 

^gg^^ 

WfflW/% 

f//W/WM 

'y/ff/t/Mffff/ 

WfflffMf/: 

W//W/M 

156 


ELECTRICITY 


lines  of  force  pass  from  the  X-pole  across,  and  into  the 
S-pole.  The  loop  of  wire  is  a  conductor ;  and  when  it 
revolves  in  this  magnetic  field,  it  cuts  the  lines  of  force, 
and  electrical  pressure  is  generated. 

190.  A.  C.  Simple  Generator.  —  Figure  144  shows  a  cross 
section  of  the  simple  generator.  Since  it  is  a  cross  section, 
the  ends  of  the  loop  of  wire,  where  it  is  cut  off,  are  dots.  In 


FIGURE  144.  —  CROSS  SECTION  OF  SIMPLE  A.  C.  GENERATOR. 

this  discussion  we  shall  mention  only  one  side  of  the  loop  of 
wire. 

Suppose  we  start  with  the  wire  at  position  a  and  turn  it 
around,  or  revolve  the  loop  at  uniform  speed. 

At  position  a  the  wire  is  moving  parallel  to  the  lines  of 
force,  and  so  does  not  cut  any.  Therefore  there  is  no  pres- 
sure being  produced.  This  can  be  shown  on  the  curve 
(Figure  145)  at  position  a. 

Now  let  the  loop  revolve  until  the  same  wire  is  at  b. 
Here  it  is  moving  perpendicular  to  the  lines  of  force,  and  so  is 
cutting  them  at  the  greatest  rate  possible.  Therefore  there 
will  be  the  greatest  pressure  generated,  —  shown  by  point  b 
on  the  curve. 

Now,  when  the  loop  revolves  so  that  the  wire  is  at  posi- 
tion c,  the  wire  is  again  moving  parallel  to  the  lines  of  force. 
Again  the  pressure  is  zero,  —  point  c  on  the  curve. 


A.    C.   SIMPLE  GENERATOR 


157 


As  the  loop  revolves  farther,  the  wire  begins  to  cut  the 
lines  of  force  in  the  opposite  direction ;  and  so  the  pressure 
will  be  in  the  other  direction,  or  will  be  negative.  When 
the  wire  reaches  position  d,  it  is  again  moving  perpendicular 
to  the  lines  of  force,  and  so  is  cutting  the  greatest  number 

-\-  Pressure 
o 


Turns 
1- 
2- 

3- 

—  Pressure 

FIGURE  145.  —  CURVE  SHOWING  PRESSURE  AT  DIFFERENT  PARTS  OF  THE 
TURN  OF  THE  ARMATURE  IN  AN  A.  C.  GENERATOR. 

again;  and  so  the  pressure  is  highest,  but  in  the  negative 
direction,  —  point  d  on  the  curve. 

When  the  loop  completes  the  turn,  the  wire  is  at  the  same 
point  as  when  it  started,  so  the  effect  is  the  same,  —  point 
c  on  the  curve. 

Reviewing  what  has  just  taken  place  throughout  the  turn, 
we  find  that  the  pressure  started  at  zero,  then  gradually 
increased  in  the  positive  direction  until  the  loop  had  made  a 
quarter  turn.  Here  the  pressure  was  the  highest,  but  imme- 
diately began  to  diminish  until  at  the  half  turn  it  had  died 
down  until  it  was  again  zero.  At  this  position  the  pressure 
began  to  increase,  but  in  the  opposite  direction,  and  con- 
tinued to  increase  until  it  reached  its  highest  value  at  the 
three-quarters  turn  ;  then  decreased  until  it  reached  zero  at 
the  complete  turn. 


158 


ELECTRICITY 


FIGURE  146.  —  PHOTOGRAPH  OF  A  HAND  GENERATOR. 


FIGURE  147.  —  PHOTOGRAPH  OF  A  300  HORSE  POWER  D.  C.  GENERATOR. 


SLIP-RINGS  159 

Thus  we  see  that  the  pressure  was  first  in  one  direction 
for  half  a  turn,  and  then  in  the  opposite  direction  for  half  a 
turn.  This  is  called  alternating  current  pressure,  and  it 
makes  the  current  flow  first  in  one  direction  throughout  the 
circuit,  and  then  stop  and  flow  in  the  other  direction. 

Alternating  Current  (A.  C.)  is  an  electrical  current  that 
flows  first  in  one  direction  and  then  in  the  other. 

Direct  Current  (D.  C.)  is  an  electrical  current  that  flows  in 
the  same  direction  all  the  time. 

191.  Slip-rings.  —  From  the  above  discussion  we  see 
that  whenever  a  loop  of  wire  revolves  in  a  magnetic  field, 


FIGURE    148.  — -  SLIP-RINGS   AND   WHERE  THEY    ARE 
PLACED  ON  THE  ARMATURE  OF  AN  A.  C.  MACHINE. 

an  alternating  current  is  produced  in  the  loop,  which  is 
called  the  armature.  If  this  current  is  taken  off  just  as  it  is 
produced,  the  current  will  be  alternating,  throughout  the 
outside  circuit.  Current  is  sometimes  taken  off  by  means  of 
slip-rings.  Slip-rings  are  two  continuous  rings  of  metal  put 
on  the  end  of  the  armature,  as  is  shown  in  Figure  148. 

The  ends  of  the  coil  are  fastened  on  these  rings,  one  end 
on  one  ring  and  the  other  end  on  the  other  ring.  iVletal  or 
carbon  "brushes"  rest  on  these  rings  and  pick  the  current 
off  just  as  it  is  made,  thus  producing  an  A.  C.  current  in 
the  external  circuit. 


160 


ELECTRICITY 


192.   D.  C.  Simple  Generator.  —  The  D.  C.  simple  gen- 
erator is  the  same  as  the.  A.  C.  simple  generator,  except  in 
the  way  the   current    is   taken   off.     In  the 

OA.  C.  generator  it  is  taken  off  by  slip-rings, 
while  in  the  D.  C.  generator  it  is  taken  off 
FIGURE  149.  —  A  by  SL  commutator. 

COMMUTATOR  Is       193.    Commutator.  —  A  commutator  is  the 
A    SLIP-RING  r       •  xu  i  i*.  •          7-j 

CUT  IN  PARTS     same  as  one  slip-ring,  except  that  it  is  split. 

It  consists  of  two  or  more  segments,  as  is 
shown  by  Figure  149. 

This  is  put  on  the  end  of  the  armature  instead  of  the  slip- 
rings.  One  end  of  the  loop  of  wire  is  fastened  to  one  seg- 
ment, while  the  other  end  of  the  wire  is  fastened  to  the 
other  segment.  "  Brushes  "  are  placed  against  these  seg- 
ments to  take  off  the  current. 


FIGURE  150.  —  A  LARGE  GENERATOR  AT  NIAGARA  FALLS,  DRIVEN  BY 
WATER  TURBINE. 


COMMUTATOR  161 

Since  the  current  alternates  in  the  loop  of  wire,  first  one 
commutator  segment  is  positive  (i.e.  the  current  comes  out), 
and  then  the  other.  But  the  brushes  are  so  set  that  when 
the  current  changes  in 
the  loop,  the  brushes  slip 
from  one  segment  to  the 
other;  thus  one  brush 
is  always  positive,  and 

the  other  is  always  nega-  ° 

TT  Vr-i         MT       FIGURE  1 51.  —  How  THE  COMMUTATOR 

tivc.     Figure  ^151    will  MAKES  A  c  BECOME  a  c> 

help  to  show  this  change. 

In  position  a,  number  1,  commutator-bar  is  on  the  right, 
and  is  negative,  while  number  2  bar  is  on  the  left,  and  is 
positive.  This  makes  the  upper  brush  positive,  and  the 
lower  brush  negative. 

In  position  b,  the  coil  has  turned  one-half  the  way  round, 
putting  number  1  on  the  left  and  number  2  on  the  right ;  but, 
in  turning,  the  current  is  reversed,  so  that  now  number  1  is 
positive  and  number  2  is  negative.  This  still  leaves  the  upper 
brush  positive  and  the  lower  brush  negative. 

-|-  Pressure 


0  M  I  m      Turns  3 

FIGURE    152.  —  CURVE  SHOWING  THE  PRESSURE  AT  DIFFER- 
ENT PARTS  OF  THE  TURN  OF  THE  ARMATURE  IN  A  D.  C. 
—  Pressure  GENERATOR. 


In  position  c,  the  conditions  are  the  same  as  in  a.  This 
shows  that  the  current  always  comes  out  of  the  same  brush, 
or  has  become  D.  C. 


162  ELECTRICITY 

194.  Curve  for  D.  C.  —  Referring  back  to  Figure  145,  the 
curve  for  the  simple  generator,  we  see  that  the  curve  changes 
somewhat  when  the  commutator  is  put  on.  It  changes  to 
the  curve  on  the  preceding  page.  (Figure  152.) 

The  first  half-turn  is  the  same,  but  the  second  half-turn 
becomes  positive,  due  to  the  fact  that  the  brushes  slip  from 

one  bar  to  the 
other  at  the  same 
time  the  current 
changes  direction. 
195.  A  Pulsat- 

FIGURE  153.  —  CROSS  SECTION  OF  A  GENERATOR       . 

WITH  3  COILS.  mg   D-   c-   Made 

Steady.  — •  From 

the  curve  (Figure  152)  we  see  that  the  current  rises  and 
falls  with  each  half-turn  of  the  loop  of  wrire.  This  is  what 
is  called  a  pulsating  current.  But  if,  instead  of  one  coil  of 
wire,  several  coils  are  put  on,  as  in  Figure  153,  then  the 

-|-  Pressure 

<•''     '^-S       "^  "V        "V  \S        V         "V        "\/ 

/XxXx>C<A 


Mi  1  IX      Turns  2 

FIGURE  154.  —  CURVES  SHOWING  PRESSURE  FROM  THREE  COILS. 
The  resulting  pressure  is  represented  by  the  tops  of  the  curves. 

current  becomes  steady.  The  reason  for  this  is  easily  seen. 
There  is  never  an  instant  when  some  coil  is  not  cutting 
the  lines  of  force  at  right  angles,  thus  constantly  keeping 
the  pressure  at  the  highest.  (Figure  154.) 


CHAPTER   XV 


MAGNETIC   EFFECT   OF   AN   ELECTRICAL   CURRENT 

196.  Magnetic  Field  about  a  Wire  Carrying  a  Current.  — 
We  have  seen  that  cutting  lines  of  force  by  a  conductor 
produces  electrical  pressure.  On  the  other  hand,  a  current 
of  electricity,  like  a  magnet,  has  about  it  a  magnetic  field. 

If  a  wire  carrying  a  current  of  electricity  be  passed  through 
a  cardboard  (Figure  155),  and  iron  filings  be  sifted  on  the 
cardboard,  the  filings 
will  arrange  them- 
selves, in  concentric 
circles,  about  the 
wire.  This  shows  that 
the  current  has  a 
magnetic  field,  and 
that  the  lines  of  force 
are  in  concentric 
circles. 

To  determine   the 
direction      of      these 

lines,  use  this  rule :  Grasp  the  wire  with  the  right  hand,  the 
thumb  in  the  direction  of  the  current,  and  the  fingers  will  point 
out  the  direction  of  the  lines  of  force.  A  magnetic  needle  set 
on  the  cardboard  will  also  show  the  direction  of  lines  of 
force.  (Figure  156.) 

If  a  wire  carrying  a  current  be  held  over  a  magnetic  needle, 

163 


FIGURE   155.  —  THE  FIELD  ABOUT  A  WIRE 
CARRYING  AN  ELECTRIC  CURRENT. 


164 


MAGNETIC  EFFECT  OF   CURRENT 


the  needle  will  tend  to  turn  at  right  angles  to  the  wire.    (Figure 
157.)     The  following  rule  can  be  used  to  tell  which  directipn 

_  the  needle  will  turn : 
Extend  the  fingers  of 
the  right  hand  along  the 
wire  with  the  wire  be- 
tween the  palm  of  the 
hand  and  the  needle, 
and  the  thumb  will 
point  the  direction  the 
N-pole  of  the  needle 
will  turn. 

197.  Currentthrough 
a  Helix.  —  A  helix  is 
a  coil  of  wire  wound 

round  and  round  in  a  spiral.     It  may  have  a  core,  or  it 
may  not.     Let  us  use  a  piece  of  soft  iron  for  a  core.     Now, 

Current 


FIGURE  156.  —  MAGNETIC  NEEDLES  SHOW  DI- 
RECTION OF  FIELD  ABOUT  A  WIRE  CARRYING 
AN  ELECTRIC  CURRENT. 


Needle 
FIGURE  157.  —  MAGNETIC  NEEDLE  TURNS  WITH  THE  LINES  OF  FORCE. 

wrhen  a  current  is  passed  through  the  helix,  it  makes  the 
iron  a  magnet  with  a  north  and  a  south  pole.     (Figure  158.) 

The  coil  would  become 
whether    the 
it  or  not, 


A A 


UU 

~u — b — D — tr 


a  magnet 
iron  were  in 
but  the  soft  iron  makes 
the  magnet  much 
stronger.  Why  ? 

To  determine  the  north  pole  of  an  electro-magnet  (for  that 
is  what  the  coil  is  called),  use  this  rule :   Grasp  the  coil  with 


FIGURE  1 58.  —  DIAGRAM  SHOWING  POSI- 
TIONS OF  POLES  OF  AN   ELECTRIC  MAGNET. 


DOORBELL  AND  BUZZER 


165 


the  right  hand  with  the 
fingers  in  the  direction  of 
the  current,  and  the  thumb 
will  point  to  the  north 
pole. 

Note  that  the  position 
of  the  north  pole  is  de- 
termined by  the  direc- 
tion which  the  current 
takes  around  the  coil. 
The  fact  that  the  current 
goes  in  at  one  end  or  the 
other  has  nothing  to  do 
with  the  north  pole. 

198.  Electro-magnet. 
-  For  a  definition  of  an 

electro-magnet  we  can 
give  this :  An  electro- 
magnet is  a  magnet 
formed  by  a  current  passing  around,  or  near,  the  magnet. 

APPLICATIONS   OF  THE  ELECTRO-MAGNET 

199.  Doorbell  and  Buzzer.  —  The  doorbell  is  one  of  the 
most  common  applications  of  the  electro-magnet.     The  cur- 
rent is  started  at  the  battery  (B,  Figure  160) ;  goes  through 
the  coils  C,  C ;  then  into  the  vibrator  V ;  then  into  the  set- 
screw  S;   then  into  the  push  button  P;   and,  finally,  back 
into  the  battery,  forming  a  complete  circuit. 

When  the  push  button  P  is  held  down,  the  current  flows 
through  the  circuit,  magnetizing  the  coils  C,  C.  These 
coils  then  attract  the  soft  piece  of  iron  on  the  vibrator,  pull- 
ing it  away  from  contact  with  -S,  and  striking  the  bell  with 


FIGURE  159.  —  PHOTOGRAPH  OF  A  2-ToN 
LIFTING  MAGNET. 


166 


MAGNETIC  EFFECT  OF  CURRENT 


•Vi 

D 

;p 

\  \ 

V 

V 

c\ 

\   X    \       1 

^ 

c\  i  i  \  \  \    i 

the  hammer.     As  soon  as  contact  is  broken,  the  coils  lose 
their  magnetism,  and  the  vibrator  flies  back  in  contact  with 

S,  due  to  the  spring  in 
the  vibrator.  As  long  as 
the  button  is  held  down, 
this  operation  is  repeated 
again  and  again,  causing 
a  steady  ringing  of  the 
bell. 

A  buzzer  is  simply  a 
doorbell  with  the  bell  left 
off.  The  buzzing  sound 
is  made  by  the  vibrator. 

200.  The  Telegraph 
Sounder.  —  The  telegraph 
sounder  consists  of  two  coils  of  wire  (C,  C)  and  a  soft  iron 
bar  (SI)  supported  on  a  pivot  (P)  in  such  a  manner  that  a 
spring  (S)  holds  the  end  of  a  bar  up 
against  a  screw  (D).  (Figure  162.) 

D 


FIGURE  160.  —  WIRING  DIAGRAM  CF 
ELECTRIC  DOORBELL. 


FIGURE  161.  —  PHOTO- 
GRAPH OF  ELECTRIC 
DOORBELL. 


FIGURE  162.  —  WIRING  DIAGRAM  OF  THE 
TELEGRAPH  SOUNDER. 


When  a  current  is  sent  through  the  coils  C,  C  by  attach- 
ing a  battery  at  A  and  B,  these  coils  become  magnets  and 
pull  the  soft  iron  bar  down  until  it  strikes  the  screw  E, 


THE    TELEGRAPH   SYSTEM 


167 


FIGURE  1 63.  —  PHOTOGRAPH  OF  THE 
TELEGRAPH  SOUNDER. 


making  a  slight  sound.  The  bar  is  held  in  this  position  as 
long  as  the  current  flows ;  but  as  soon  as  the  current  stops, 
the  coils  lose  their  magnetism,  and  the  bar  flips  back  to  D, 
making  a  loud  click.  By 
means  of  these  sounds, 
the  operator  is  able  to 
read  the  message. 

201.   Telegraph  Relay. 
-  The    telegraph    relay 
merely  uses  the  electro- 
magnet to  close  another 
electric  circuit. 

The    main   current    is 
sent  through  coils  C,  C 

(Figure  164)  by  connecting  the  main  line  to  A  and  B. 
This  magnetizes  the  coils,  and  they  attract  the  soft  bar  of 
iron  SI,  pulling  it  up  into  contact  with  screw  E.  This 
completes  the  circuit  between  C  and  D,  the  binding- 
posts  for  the  local  circuit. 

202.  TheTele- 
"  ^nsulated  graph  System.  - 
We  have  just 
learned  the  con- 
struction of  the 
sounder  and  re- 
lay, so  now  we 
will  see  how  they 
are  put  to  use  in 
the  telegraph 
system. 

Figure    167   shows   a   system   through   three   cities.     At 
Chicago  the  main  wire  is  grounded ;   then  a  battery  (B)  is 


37 

•:5J 

1   \ 

lev    \   i  s 

« 

1    \ 

\c\   \    i| 

V, 

Jl 

FIGURE   1 64.  —  WIRING  DIAGRAM  OF  THE 
TELEGRAPH  RELAY. 


168 


MAGNETIC  EFFECT  OF   CURRENT 


put  in ;  and  also  a  key  (K)  and  a  relay  (R).     Next,  the  wire 
runs  to  Toledo ;   and  again  a  key  and  a  relay  are  connected 

in  series  with  the  line.  It 
goes  then  to  Cleveland, 
where  still  another  key, 
relay,  and  battery  are  put 
in.  Then  the  wire  is 
grounded.  This  com- 
pletes the  main  circuit. 

Tracing  the  circuit,  we 
start  at  the  ground  at  Chicago,  go  through  the  battery, 
relay,  and  key  to  the  key,  and  relay  at  Toledo,  then  through 


FIGURE  165.  —  PHOTOGRAPH  OF  THE 
TELEGRAPH  RELAY. 


FIGURE  166.  —  PHOTOGRAPH  OF  A  TELEGRAPH  KEY. 

the  key,  relay,  battery,  and  ground  at  Cleveland,  returning 
through  the  ground  to  Chicago. 

Off  each  relay  is  run  a  local  circuit,  in  which  are  a  battery 


—     Chicago 
EB 


FIGURE  167.  —  WIRING  DIAGRAM  OF  A  THREE  STATION  TELEGRAPH  SYSTEM. 


STREET   CAR   CIRCUIT-BREAKER  169 

and  a  sounder.     The  relay  closes  the  local  circuit ;   and  the 
battery  sends  a  current  through  the  sounder,  making  it  click. 

Note  that  the  current  in 
the  main  line  never  goes 
through  the  sounder. 

203.  The  Electric  Clock. 
-  Very  often  it  is  desired 

to  have  several  clocks  run 

exactly  together ;  in  other 

i  ,  11   j  i  FIGURE  168.  —  WIRING  DIAGRAM  OF 

words,  to  be  controlled  by  ELECTRIC  CLOCK 

a    master-clock.      This    is 

accomplished  by  the  so-called  electric  clock.     (Figure  168.) 

The  clock  consists  of  a  pair  of  coils  (C,  C)  so  arranged 
that  when  an  electric  current  passes  through  them  they 
turn  the  soft  iron  (SI)  on  the  pivot  (P),  making  the  pawl 
(R)  slip  down  a  notch  on  the  ratchet  wheel.  Then,  when 
the  current  is  stopped,  the  weight  (W)  turns  the  bar  back, 
pushing  the  wheel  around  one  notch.  This  takes  place 
every  minute,  thus  making  the  minute  hand  move  one 
space  on  the  dial. 

For  sending  the  current  through  the  coils  an  electric  cir- 
cuit is  made  through  the  master-clock.  The  master-clock 
runs  a  drum  (D,  Figure  168)  on  which  is  a  peg  (0).  The 
peg  touches  the  point  S  every  minute,  thus  making  a  com- 
plete circuit  through  the  battery  and  electric  clock. 

204.  Street  Car  Circuit-breaker.  —  As  a  safety  device  a 
so-called  circuit-breaker  is  put  on  street  cars.     Its  purpose 
is  to  break  the  circuit  whenever  the  current  becomes  too 
large.     It  is  constructed  as  in  Figure  169. 

The  current  from  the  trolley  comes  into  the  point  a ;  then 
goes  through  the  coil  C ;  then  to  the  arm  A  ;  and  out  of 
the  contact  K  by  point  6.  The  current  makes  a  magnet  of 


170 


MAGNETIC  EFFECT  OF   CURRENT 


'/£        v-.   QH  j 

c 

5j 

^c 

US1 


FIGURE  169.  —  WIRING  DIAGRAM  OF  CIRCUIT- 
BREAKER. 


the  coil,  its  strength  depending  on  the  size  of  the  current. 
If  the  current  becomes  sufficiently  strong,  it  lifts  the  soft 

a  iron  bar  SI,  tripping 
the  hook  H,  allowing 
the  spring  S  to  pull 
up  the  arm  A,  thus 
breaking  the  circuit. 
The  motorman  must 
then  reach  up  and  pull 
down  the  arm  again 
before  he  can  start  the 
car. 

205.  The  Annunci- 
ator. —  The  annunci- 
ator is  an  instrument 
used  in  office  buildings,  in  elevators,  etc.,  etc.,  for  the  pur- 
pose of  telling  at  what 
place  the  person  calling 
is  located.  There  may 
be  any  number  of  push- 
buttons, but  the  dia- 
gram (Figure  171)  shows 
an  elevator  call-system 
for  four  floors,  or  for 
four  push-buttons. 

In  the  annunciator  are 
four  coils  (c,  c,  c,  c),  five 
binding-posts  (a,  b,  c,  d, 
and  e),  and  the  door- 
bell (B). 

From  the  binding- 
posts  a,  6,  c,  d  run  wires 


FIGURE  170.  —  PHOTOGRAPH  OF  A  CIRCUIT- 
BREAKER. 


THE  AUTOMATIC  ARC  LAMP 


171 


B 


f 


-UL 


FIGURE  171.  —  WIRING  DIAGRAM 
OF  A  FOUR-POINT  ANNUNCIATOR. 


through  coils  1,  2,  3,  4,  respectively,  these  wires  all  being 
connected  with  one  wire  which  runs  to  the  bell  and  finally 
to  the  binding-post  e.  This  con-  D 

stitutes  the  internal   connection 
of  the  annunciator. 

The  external  connections  are 
as  follows  :  A  battery  is  attached 
to  the  binding-post  e,  and  then  a 
single  wire  is  run  up  to  all  of 
the  succeeding  push-buttons. 
Then  from  each  push-button  re- 
turns a  wire  to  its  respective 
binding-post,  a,  b,  c,  or  d. 
Whenever  a  push-button  is 

pushed,  it  completes  the  circuit,  through  the  corresponding 
coil  and  also  the  bell.  Thus  the  bell  is  rung,  and  the  needle 
below  the  magnet  is  drawn  over,  indicating  which  push- 
button was  operated. 

206.  The  Automatic  Arc  Lamp.  —  The  automatic  arc 
lamp,  which  is  used  principally  to  light  our  streets  and  large 
factory  buildings,  is  an  application  of  the  electro-magnet. 

This  principle  is  used 
automatically  to  ad- 
just the  carbons,  which 
are  continually  burn- 
ing off.  To  light  the 
arc,  the  carbons  must 
first  touch ;  and  then 
must  be  drawn  just  the 
correct  distance  apart, 

FIGURE  172.  — WIRING  DIAGRAM  OF  AN          anc*  *ept  tnere'      ine 

AUTOMATIC  ARC  LAMP.  operation  is  as  follows : 


172  MAGNETIC  EFFECT  OF   CURRENT 

The  current  flows  from  the  line  into  coil  Ci  (Figure  172), 
and  then  divides.  One  part  goes  to  the  upper  carbon,  and 
the  other  part  goes  to  the  coil  C2. 

When  the  lamp  is  not  lighted,  the  upper  carbon  falls 
down  and  touches  the  lower  one;  thus  when  the  current 
first  starts,  nearly  all  of  it  flows  through  the  carbons,  instead 
of  through  lower  coil  C2,  for  the  resistance  of  the  carbons  is 
much  less  than  that  of  coil  (72.  Thus  upper  coil  Ci  is  mag- 
netized, but  lower  coil  C2  is  not.  This  pulls  the  soft  iron 
bar  $7  up,  and  also  the  upper  carbon  which  is  attached  to  it. 

As  the  carbons  are  separated,  the  light  is  formed,  and  at 
the  same  time  the  resistance  of  the  gap  becomes  more  and 
more,  forcing  part  of  the  current  to  flow  through  coil  C2. 
Whenever  this  part  becomes  strong  enough  to  balance  the 
pull  of  coil  Ci,  the  carbons  are  held  stationary. 

207.  Other  Applications  of  the  Electro-magnet.  —  Other 
applications  of  the  electro-magnet  are  the  automatic  tele- 
phone, the  electric  gas-lighter,  and  the  electric  door-latch. 

The  automatic  telephone  takes  the  place  of  the  operator 
at  the  switchboard.  The  person  calling  does  so  by  pressing 
on  a  dial  at  his  transmitter,  thus  calling  the  number  he 
wishes.  No  telephone  operator  is  necessary  to  make  the 
connection,  as  the  electro-magnets  do  it  automatically. 

The  gas-lighter  consists  of  two  electro-magnets,  —  one 
to  turn  on  the  gas  and  light  it,  and  the  other  to  turn  the 
gas  off.  It  is  used  where  it  is  desirable  to  turn  the  gas  off 
and  on  from  some  other  place  than  at  the  jet. 

The  electric  door-latch  is  used  principally  in  apartment 
houses,  and  is  so  arranged  that  the  outer  door  may  be  opened 
by  pressing  a  button  in  any  of  the  apartments.  The  pressing 
of  the  button  closes  an  electric  circuit,  causing  an  electro- 
magnet to  release  the  latch  of  the  door. 


CHAPTER  XVI 
HEATING  EFFECT   OF  AN   ELECTRIC   CURRENT 

208.  Work,  Heat,  and  Electrical  Energy.  —  Work  is   de- 
fined as  a  force  overcoming  a  resistance  and  moving  it. 
Work  is  energy,  and  so  is  heat.     There  are  many  cases 
where  work  is  changed  into  heat.     If  you  slide  down  a  rope, 
it  burns  your  hands.     Your  weight  forces  you  down  against 
the  friction  of  your  hand  on  the  rope,  thus  doing  work; 
and  this  work  is  changed  to  heat.     Again,  if  a  piece  of  iron 
is  hammered,   it  becomes  warm.     If  you  stir  cake-dough 
rapidly  for  some  time,  it  becomes  warmer.     The  work  you 
do  is  transformed  into  heat. 

The  same  thing  is  true  when  a  current  of  electricity  is 
forced  through  a  wire.  The  pressure  is  the  force ;  the  cur- 
rent is  the  thing  forced;  and  the  resistance  of  the  wire  is 
the  thing  that  holds  the  current  back.  It  is  just  like  your 
weight  forcing  your  body  down  the  rope  against  the  friction  ; 
and,  as  in  that  case,  heat  is  produced. 

Learn  this  important  principle :  When  an  electrical  pres- 
sure forces  an  electrical  current  through  a  resistance,  heat  is 
generated. 

209.  Electrical  Units.  —  Electrical  quantities  are  definite, 
just  like  distance,  weight,  time,  etc.;  so  it  is  necessary  to  have 
units  to  measure  them. 

The  following  table  gives  the  thing  to  be  measured,  the 
unit  of  measurement,  and  the  letter  used  to  stand  for  it : 

173 


174 


HEATING    EFFECT    OF    CURRENT 


THING  TO  BE  MEASURED 

UNIT 

LETTER 

Volt 

E 

Current    

Ampere 

I 

Resistance 

Ohm 

R 

Power 

fWatt 

W 

Electrical  Energy       .     .     .     . 

|  Kilowatt 
[  Watt-hour  . 
1  Kilowatt-hour 

Kw 

W-hr. 
Kw-hr. 

It  will  be  noted  that  power  is  a  new  term,  and  that  it  has 
two  units  —  watt  and  kilowatt.  The  kilowatt  is  the  larger 
unit,  and  is  1000  watts. 

Electrical  power  is  the  time  rate  of  delivering  electrical  energy. 

The  electrical  power  is  found  by  multiplying  the  pressure 
by  the  current ;  or 

Watts  =  Volts  X  Amperes. 
W  =  E  •  I. 

Number  of  Kilowatts  =  N™b«rof  Vdts  Dumber  of  Amperes 

1000 


or  Kw  = 


E-I 

1000 


The  electrical  energy  is  found  by  multiplying  the  power 
by  the  time,  or 

Watt-hours  =  Watts  X  Hours. 

W-hr.  =  WXt. 

Kiloivatt-hours  =  Kiloivatts  X  Hours. 

Kw-hr.  =  KwXt. 

The  terms  electrical  power  and  electrical  energy  are  often 
confused.     Be  sure  to  get  the  distinction. 

Electrical  power  is  the  rate  of  delivering  energy.      It  is 


OHM'S  LAW  175 

the  pressure  at  a  certain  instant   X  the  current  at  the  same 
instant. 

On  the  other  hand,  electrical  energy  is  a  certain  amount  of 
energy  which  is  actually  delivered.  It  is  not  the  rate  of 
delivering  the  energy,  but  is  the  energy  itself.  The  power 
must  work  for  a  certain  time  to  give  energy.  Which  do  you 
pay  for  when  you  pay  your  light  bill,  power  or  energy? 
Does  it  make  any  difference  whether  a  40-watt  lamp  burns 

1  hour  or  3  hours? 

Problems 

1.  What  power  is  being  used  when  a  carbon  lamp  taking  .5  ampere 
is  placed  on  a  110- volt  circuit? 

2.  What  is  the  power  used  when  an  iron  takes  5^  amperes  on  110 
volts? 

3.  State,  in  words,  how  to  find  the  power  in  watts  and  in  kilowatts, 
having  given  the  current  and  voltage. 

4.  Find  the  cost  of  running  ten  40-watt  lamps  for  5  hours,  if  elec- 
tricity costs  10  cents  per  Kw-hr. 

6.  Figure  your  monthly  light  bill,  if  you  run,  on  an  average,  4  lamps 
of  40  watts  each,  three  hours  each  day ;  an  iron  taking  5  amperes  for 

2  hours,  4  times  a  month ;   and  a  motor  taking  3  amperes  for  1  hour, 
10  times  a  month.     Your  lighting  circuit  is  110  volts,  the  month  has 
30  days,  and  the  price  of  electricity  is  9  cents  per  Kw-hr. 

210.  Ohm's  Law.  —  A  great  scientist  by  the  name  of 
Ohm  worked  out  this  very  fundamental  law,  known  as 
Ohm's  Law: 

Voltage  =  Current  X  Resistance,  or 
E  =  I  -  R.  (1) 

Which  may  also  be  written : 

I  =  E  (2) 

R 

R  =  (3) 


176  HEATING   EFFECT    OF    CURRENT 

By  these  three  equations  it  is  possible  to  find  voltage,  cur- 
rent, or  resistance,  if  the  other  two  quantities  are  given. 
Always  be  sure  to  choose  the  one  which  will  answer  the 
question  to  your  problem. 

Problems 

1.  What  current  will  a  lamp  take  on  a  110- volt  circuit,  if  its  resist- 
ance is  220  ohms? 

2.  What  current  would  the  lamp  above  take  if  placed  on  a  220-volt 
circuit  ? 

3.  What  current  would  a  lamp  take  on  a  110- volt  and  a  220-volt 
circuit,  respectively,  if  its  resistance  were  44  ohms  ? 

4.  What  voltage  is  necessary  to  send  6  amperes  through  an  iron,  if 
its  resistance  is  15  ohms? 

6.  What  is  the  resistance  of  a  stove,  if  it  takes  5.5  amperes  on  110 
volts? 

6.  The  resistance  of  the  hea  ing-element  of  an  iron  increases  when 
it  gets  hot.     When  does  it  take  more  current,  hot  or  cold  ? 

7.  A  carbon  lamp  takes  .5  ampere  on  a  110- volt  circuit,  while  a 
tungsten  takes  .315  ampere  on  the  same  circuit.     Which  one  has  the 
higher  resistance,  and  how  much  ? 

8.  A  dimmer  on  a  lamp  cuts  the  current  down  from  .315  ampere 
to  .2  ampere.     What  is  the  resistance  of  the  dimmer,  if  the  lamp  is 
on  a  110- volt  circuit? 

APPLICATION  OF  HEATING    EFFECT  OF    AN  ELECTRIC 

CURRENT 

211.  The  Carbon  Incandescent  Lamp.  —  The  carbon  in- 
candescent lamp  was  one  of  the  first  electric  lamps  used,  and, 
like  all  the  later  lamps,  it  uses  the  heating  effect  of  an  elec- 
trical current  to  produce  the  light,  the  principle  being  to 
force  a  large  enough  Current  through  a  carbon  wire  to  heat 
it  to  incandescence. 

The  lamp  consists  of  a  glass  bulb  from  which  the  air  has 
been  exhausted.  (Figure  173.)  Inside  the  bulb  is  the  carbon 


THE   TUNGSTEN  INCANDESCENT  LAMP 


177 


wire  through  which  the  current  must  pass.  This  wire  makes 
connection  through  the  end  of  the  bulb  by  means  of  small 
pieces  of  platinum  wire,  platinum  being 
used  because  its  coefficient  of  linear  ex- 
pansion is  nearly  that  of  glass.  Other 
materials  would  cause  the  glass  to  break 
when  it  was  heated  or  cooled. 

The  glass  bulb  is  sealed  with  wax  into 
a  screw  tip,  —  one  end  of  the  wire  being 
attached  to  the  side  of  the  tip,  while  the  FlGURE  173.  — WIR- 

.  ING  DIAGRAM  OF  A 

other  is  attached  to  a  small  piece  set  in       CARBON  LAMP. 

the  middle   of   the   tip.     By  this  means 

the  two  ends  of  the  wire  are  insulated  from  one  another. 

Contact  is  made  through  the  lamp  by  screwing  it  into  a 

lamp-socket.  The  screw  of  the 
socket  is  one  side  of  the  line,  and 
the  middle  portion  is  the  other 
side  of  the  line. 

Carbon  lamps  can  be  used  on 
either  D.  C.  or  A.  C.  They  are 
made  for  almost  any  voltage 
(although  care  must  be  taken  to 
get  the  correct  voltage  for  the 
circuit  in  question),  and  take 
about  3-g-  watts  per  candle  power. 
212.  The  Tungsten  Incandes- 
cent Lamp.  —  This  lamp  is  con- 
structed like  the  carbon  lamp, 
except  that  the  wire  filament  is 

made    of   tungsten   instead  of   carbon.     Figure  175  shows 

the  tungsten  lamp. 

The  tungsten  has  almost  replaced  the  carbon  lamp,  for  it 


FIGURE   1 74.  —  PHOTOGRAPH 
OF  A  CARBON  LAMP. 


178 


HEATING    EFFECT    OF    CURRENT 


FIGURE  175.  — WIR- 
ING DIAGRAM  OF  A 
TUNGSTEN  LAMP. 


takes  about  one- third  as  much  electrical  power  to  light  it  and 
costs  very  little  more  for  the  lamp  itself.  The  objection  at 
first  to  the  tungsten  lamp  was  that  its 
filament  was  so  fragile. 

The  filaments  of  the  first  lamps  were 
made  by  grinding  the  tungsten  to  a 
powder,  making  a  paste  of  it  and  squeez- 
ing it  through  holes,  and  then  baking  it. 
These  filaments  broke  with  the  least  jar. 
Lately  manufacturers  have  learned  to 
draw  the  tungsten  metal  into  wires  for 
filaments,  and  these  are  even  more  dur- 
able than  the  old  carbon  filaments. 

This  lamp  can  be  used  the  same  as  the  carbon  lamp, 
but  it  takes  only  about  Ij  watts  per  candle  power. 

213.  The  Gas-filled  Lamp.  — The 
gas-filled  lamp  is  a  tungsten  lamp 
with  the  bulb  filled  with  a  gas,  usually 
argon  or  nitrogen,  instead  of  having  it 
a  vacuum.    The  filament  is  put  into  a 
more  compact  coil,  so  that  this  lamp 
is  used  especially  with  a  reflector. 

The  gas-filled  lamp  can  be  used  in 
any  place  that  the  carbon  or  tungsten 
can,  and  takes  about  1  watt  per 
candle  power. 

Lamps  of  100  watts  rating,  or  over, 
are  usually  filled  with  nitrogen,  while 
lamps  of  lower  ratings  are  usually 
filled  with  argon. 

214.  The  Mercury  Vapor  Lamp.— This  lamp  consists  of 
a  long  glass  tube,  nearly  exhausted  of  air  and  containing 


FIGURE  1 76.  —  PHOTOGRAPH 
OF  A  TUNGSTEN  LAMP. 


THE  ARC  LAMP  179 

a  small  quantity  of  mercury.  In  each  end  platinum  wires 
are  sealed,  making  connections  with  the  electric  circuit. 
(Figure  177.) 

To  light  the  lamp,  the  tube  is  brought  to  a  horizontal 
position,  so  that  the  mercury  makes  contact  from  one  end 
of  the  tube  to  the  other.  As  soon  as  contact  is  made,  the 
tube  is  tilted  so  as  to  make  the  mercury  flow  to  one  end. 
This  breaks  contact,  and  at  this  point  the  mercury  is  vapor- 
ized by  the  heating  effect.  This  vapor  fills  the  tube,  acting 
as  a  conductor  for  the  current.  The  current  passing  through 
the  vapor  heats  it  to  in- 
candescence, giving  off  a 
bluish-green  light.  Some 
mercury  vapor  lamps  are 
lighted  by  other  means 

than  tilting,  but  they  all 

FIGURE  177.  —  WIRING  DIAGRAM  OF  A 
use  the  same  principle  for  MERCURY  VAPOR  LAMP. 

producing  the  light. 

This  lamp  is  used  especially  in  lighting  large  buildings, 
such  as  factories ;  for  taking  photographs ;  and  for  rectify- 
ing A.  C.  electricity  for  storage  batteries. 

215.  The  Arc  Lamp.  —  We  have  already  spoken  of  the 
arc  lamp  (Figure  172),  but  since  it  is  an  application  of  the 
heating  effect  of  an  electrical  current,  as  well  as  of  an  electro- 
magnet, we  mention  it  here. 

The  method  of  lighting  is  very  much  the  same  as  in  the 
mercury  vapor  lamp.  To  light  it,  the  carbons  must  touch, 
allowing  the  current  to  flow  through  them.  Then  the  car- 
bons must  be  pulled  apart,  breaking  the  electric  circuit. 

At  the  point  where  the  circuit  is  broken,  a  high  resistance 
is  entered.  The  current  flowing  through  this  high  resist- 
ance produces  heat  sufficient  to  vaporize  the  carbon  at  that 


180 


HEATING   EFFECT    OF    CURRENT 


FIGURE  178.  —  DIA- 
GRAM OF  ELECTRIC 
FLAT-IRON. 


point.     This  carbon  vapor  acts  as  the  conductor,  and  is 

heated  to  incandescence,  giving  off  a  very  bright  and  power- 
ful light.  The  temperature  reaches  as 
high  as  3500°  C.  and  gives  about  1  candle 
power  per  watt. 

Arc  lamps  are  used  to  light  streets  and 
large  buildings.  They  are  usually  placed, 
100  lamps  in  a  series,  on  a  5000-volt  line, 
taking  from  6  to  9  amperes.  They  will 
work  either  on  A.  C.  or  D.  C. 

In  moving-picture  houses  the  arc  lamp  is 

used  in  the  picture  machine.     These  arcs  usually  take  from 

50  to  100  amperes,  as  a  very  high  candle 

power  is  desired. 
216.  The     Electric     Flat-iron.  —  The 

electric    flat-iron    (Figure    178)    is   very 

much  like  the  ordinary  flat-iron,  except 

that   it   has  a  heating  element  and  an 

attachment  to  connect  it  to  the  lighting  FIGURE  179. —  HEAT- 
ING ELEMENT  IN  AN 

system.  ELECTRIC  FLAT-IRON. 

The  heating  element  is  a  special  kind 

of  wire  of  high  resistance  wound  on  an  insulator  and  placed 

inside  the  iron. 
Very  often  ni- 
chrome  wire  is 
wound  on  a  piece 
of  mica  (Figure 
179),  and  this  is 
then  placed  be- 
tween sheets  of 

FIGURE  1 80.  —  PHOTOGRAPH  OF  ELECTRIC  mica'      Tne     miCa 

FLAT-IRON.  acts   as    an    insu- 


OTHER  APPLICATIONS 


181 


lator.  Connection  is  made  through  a  duplex  (double)  wire 
attached  to  a  plug,  which  can  be  screwed  into  an  ordinary 
lamp-socket. 

It  is  better,  however,  to  have  a  special  socket  for  the 
iron,  as  the  current  used  is  often  large  enough  to  burn 
out  the  connection  in  an  ordinary 
socket. 

The  pressure  forcing  the  current 
through  the  heating  element  pro- 
duces the  heat,  and  as  the  current 
is  turned  on  while  using,  the  iron 
remains  hot. 

If  the  iron  does  not  get  hot 
enough,  it  may  be  fixed  by  short- 
circuiting  one  turn  of  its  heating 
element,  thus  letting  through  more 
current.  If  it  gets  too  hot,  another 
turn  may  be  added.  Why  ? 

217.  Other  Applications. — Along 
with  the  flat-iron  come  many  other 
electrical  heating  appliances.  Some 
of  these  are  the  toaster,  curling 
iron,  stove,  coffee  percolator,  and 
soldering  iron.  Any,  and  all,  of 
these  can  be  used  on  A.  C.  or  D.  C., 
and  can  be  bought  for  different  voltages,  although  the 
standard  voltage  is  110. 

The  amount  of  current  taken  by  these  appliances  varies 
with  the  appliance.  A  toaster  usually  requires  from  1  to 
3  amperes;  a  curling  iron  from  J  to  1  ampere;  a  stove 
from  3  to  10  amperes;  a  percolator  from  2  to  5  amperes; 
and  a  soldering  iron  from  1  to  2  "amperes. 


FIGURE  181.  —  PARTS  OF  AN 
ELECTRIC  FLAT-IRON. 

1.  Cover  and  handle. 
2.  Cast  iron  plate  that 
fits  over  heating  ele- 
ment. 3.  Heating  ele- 
ment. 4.  Base  on  which 
heating  element  rests. 


182 


HEATING    EFFECT    OF   CURRENT 


FIGURE  182.  —  AN  ELECTRIC  GRILL. 
Can  be  used  for  several  methods  of  cooking. 


FIGURE  183.  —  ELECTRIC  COFFEE          FIGURE  184.  —  ELECTRIC  COOK  STOVE. 
PERCOLATOR. 


OTHER  APPLICATIONS 


183 


Electrical  heating  appliances  are  coming  more  and  more 
into  common  use,  principally  from  the  fact  that  they 
are  very  convenient  and 
at  the  same  time  are 
so  clean  and  sanitary. 
Even  the  electric  cook 
stove  is  now  quite  com- 
mon. It  has  become  so, 
largely  because  it  does 
away  with  objectionable 
coal  and  gas  fumes. 

Electric  cars  are  com- 
monly heated  by  electric 
registers,  and  electric 
heaters  are  often  used  in 
homes,  especially  to  heat 
small  rooms,  like  bath- 
rooms. During  weather 
which  is  too  warm  to 
require  a  furnace  fire, 
and  yet  is  too  cold  to 
keep  the  house  comfort- 
able without  a  little  heat,  electric  heaters  leave  the  air 
purer  than  those  which  burn  gas  or  oil. 

In  buying  any  electrical  appliance,  care  should  be  used 
to  get  a  good  one,  as  the  extra  cost  at  the  beginning  is  soon 
saved  in  the  saving  of  electrical  energy  to  run  it. 


FIGURE  185.  —  ELECTRIC  IRONING  MACHINE. 
HEATED  AND  RUN  BY  ELECTRICITY. 


CHAPTER   XVII 


MOTION-PRODUCING   EFFECT   OF   AN   ELECTRIC 
CURRENT 

218.  How  Motion  is  Produced.  —  We  saw  in  the  case  of 
a  coil  of  wire  revolved  in  a  magnetic  field  that  a  current 
was  produced  in  the  coil.  The  reverse  of  this  is  also  true. 
If  a  coil  of  wire  is  put  into  a  magnetic  field  and  a  current  is 

sent  through  the  coil, 
it  is  made  to  revolve. 
With  the  aid  of  Figure 
186  we  will  show  why 
it  will  revolve,  and  in 
which  direction  the 
motion  will  take  pla.ce. 
Let  the  current  go 
through  the  coil  in  the 
direction  ABODE 
F.  Then  the  coil  be- 
comes a  magnet  with 
its  north  pole  (Ne)  at  the  top  face  of  the  coil,  and  its  south 
pole  (Se)  at  the  bottom  face  of  the  coil. 

Now,  since  like  poles  repel  and  unlike  poles  attract,  the 
coil  is  made  to  revolve  clockwise,  or  in  the  direction  of  the 
small  arrow  at  E.  Thus  we  see  that  the  coil  is  made  to 
turn  and  that  the  turning  effect  is  due  to  attraction  and  re- 
pulsion of  magnetic  poles. 

184 


FIGURE  186.  —  How  MOTION  is  PRODUCED 
BY  ELECTRICITY. 


THE   GALVANOMETER 


185 


APPLICATION   OF   MOTION- PRODUCING   EFFECT   OF  AN 
ELECTRIC    CURRENT 

219.  The  Galvanometer.  —  The  galvanometer  is  an  in- 
strument used  to  detect  an  electrical  current  in  a  conductor. 
It  consists  of  a  coil  of  wire  (C,  Figure  187)  suspended  between 
the  poles  (N  and  S)  of  a  permanent  magnet  by  means  of  a 
phospor-bronze  ribbon 
ending  in  a  small  spring 
at  the  bottom. 

The  current  to  be  de- 
tected is  sent  through 
the  coil  making  it  an 
electro-magnet.  If  the 
current  passes  down- 
ward, as  the  arrow  in- 
dicates, the  north  pole 
of  the  coil  is  to  the 
left  of  the  coil. 

The  permanent  S-pole 
then  attracts  it,  and 
the  coil  is  made  to  turn 
as  the  arrows  indicate. 

If  it  were  not  for  the  spring,  the  coil  would  turn  until  its 
north  pole  would  be  directly  in  front  of  the  permanent 
S-pole,  and  would  then  stop.  But  the  spring  allows  it  to 
turn  only  so  far  as  the  strength  of  the  poles  forces  it.  Since 
the  strength  of  the  poles  depends  upon  the  current  flowing 
in  the  coil,  the  deflection  of  the  coil  indicates  not  only  that 
there  is  a  current,  but  its  relative  strength. 

To  make  the  reading  of  the  deflection  easy,  a  pointer  is 
attached  to  the  coil  (or  sometimes  a  mirror  is  used,  so  that 


FIGURE  187.  —  WIRING  DIAGRAM  OF  A 
GALVANOMETER. 


186      MOTION-PRODUCING  EFFECT  OF  CURRENT 


FIGURE  188. —WIRING  DIAGRAM  SHOWING  WHERE  AMMETER  AND 
VOLTMETER  ARE  PLACED. 

a  ray  of  light  may  be  deflected),  showing  the  amount  of 
deflection. 

220.  The  Ammeter.  —  The  galvanometer  detects  current 
flowing,  and  its  relative  value,  but  does  not  give  its  amount 
in  amperes. 


FIGURE  1 89.  —  PHOTOGRAPH  OF  A  VOLTMETER  WITH  THE  COVER 
REMOVED. 


THE   VOLTMETER 


187 


When  the  galvanometer  has  its  scale  graduated  in  amperes, 
it  is  called  an  ammeter.  Its  principle  is  just  the  same  as  the 
galvanometer,  but  reads  directly  in  amperes. 

The  resistance  of  the  coil  in  an  ammeter  is  very  low,  so 
that  it  must  always  be  placed  in  the  line  (A,  Figure  188), 
and  never  across  the  line. 

221.  The  Voltmeter.  —  The  voltmeter  is  also  like  the 
galvanometer,  consisting,  as  it  does,  of  permanent  magnets 


FIGURE   190. — THE  PERMANENT  MAGNET,  COIL,  AND  POINTER  OF  A 
D.  C.  VOLTMETER. 

(D.  C.  meter)  and  a  suspended  coil.     The  scale  of  the  volt- 
meter is  graduated  to  read  directly  in  volts. 


188      MOTION-PRODUCING  EFFECT  OF   CURRENT 

The  resistance  of  the  voltmeter  is  made  very  high;  so  it 
should  be  placed  across,  not  in,  the  line  (V,  Figure  188). 

This  resistance  is  made  up  of  the  resistance  of  the  mov- 
able coil  of  the  instrument.  When  a  high  resistance  is  desired 
fine  wire  with  a  large  number  of  turns  is  used,  but  when 
a  low  resistance  is  needed  the  coil  is  wound  with  a  coarse 
wire  with  few  turns. 

It  is  essential  that  you  know  how  to  connect  a  voltmeter 
and  an  ammeter  correctly.  Should  you  put  the  ammeter 


FIGURE   191. — THE  MOVABLE  COIL  AND  POINTER  OF  A  VOLTMETER. 

across  the  line,  it  will  be  burned  out.     Should  you  place  the 
voltmeter  in  the  line,  it  will  shut  off  almost  all  the  current. 

222.   The  Wattmeter.  —  The  wattmeter  is  an  instrument 
made  to  read  the  power  used  in  a  line,     It  consists  of  two 


THE   WATTMETER 


189 


FIGURE  192.  —  A  VOLT-AMMETER  WHICH  CAN  BE  USED  AS  EITHER  A 
VOLTMETER  OR  AN  AMMETER. 

The  metal  binding  posts  are  ammeter  connections,  and  the  rubber 
ones  are  voltmeter  connections. 

sets  of  coils.  One  set  takes  the  place  of  the  permanent 
magnets  in  the  ammeter,  voltmeter,  and  galvanometer,  and  the 
other  coil  is  movable,  as  in  the  above  instruments. 


Line 


Load 


FIGURE  193.  —  WIRING  DIAGRAM  OF  A  WATTMETER. 


190      MOTION-PRODUCING  EFFECT  OF   CURRENT 

Since  the  wattmeter  measures  power,  it  must  read  in 
watts,  or  wits  X  amperes. 

It  is  so  connected  (Figure  193)  that  the  current  passes 
through  the  field  coils,  measuring  the  current ;  and  the 
movable  coil  is  connected  across  the  line,  measuring  the  volts. 
The  deflection  then  reads 

Volts  X  Amperes  =  Watts. 

223.  Meters  for  A.   C.   Electricity.  —  The  meters  here 
described  are  for  D.  C.,  although  the  wattmeter  will  work 
on  either  A.  C.  or  D.  C.     But  a  special  kind  of  ammeter 
and  voltmeter  must  be  made  for  A.  C.     They  must  have 
electro-magnets,  instead  of  permanent  magnets. 

224.  D.  C.  Motors.  —  We  have  shown  how  a  loop  of  wire 
with  a  current  in  it  tends  to  revolve  when  placed  in  a  mag- 
netic field.     But  its  tendency  is  to  revolve  no  farther  than 
to  bring  the  face  of  the  coil  which  is  a  N-pole  opposite  the 
S-pole  of  the  field  magnet,  and  to  remain  in  this  position. 

Now,  if  the  current  is  reversed  in  the  coil,  the  face  which 
was  a  N-pole  becomes  a  S-pole,  and  vice-versa ;  and  the  coil 
is  made  to  revolve  another  half -turn.  If  the  current  is 
again  reversed,  the  coil  makes  another  half-turn ;  and  so  on. 
Thus  the  coil  is  made  to  turn  continuously  by  reversing  the 
current  in  the  loop  every  half -turn. 

You  will  remember  that  the  alternating  current  generated 
in  the  loop  of  wire  of  the  generator  was  made  direct  by 
means  of  a  commutator.  In  the  same  way  a  direct  current 
is  made  to  reverse  in  the  loop  of  wire  in  the  motor.  Thus 
by  putting  a  commutator  on  the  loop  of  wire  the  coil  is 
made  to  turn  continuously.  Do  not  forget  that  the  turning 
effect  is  due  to  the  attraction  of  magnetic  poles. 

The  difference  between  a  generator  and  a  motor  is  this: 


THE   WATT-HOUR   METER 


191 


the  generator  is  supplied  with  mechanical  energy,  and  trans- 
forms it  into  electrical  energy;  while  a  motor  is  supplied 
with  electrical  energy,  and  transforms  it  back  to  mechanical 
energy.  A  direct  current  generator  may  be  used  also  as  a 
motor. 

225.  The  Watt-hour  Meter.  —  The  principle  of  the  watt- 
hour  meter  is  the  same  as  the  wattmeter,  but  instead  of  the 

movable  coil  being  held     

in  position  by  a  spring 
it  is  allowed  to  turn 
around  freely,  as  a 
motor.  Geared  to  the 
movable  coil  are  small 
hands  which  pass  over 
dials,  just  as  in  the  gas- 
meter. 

With  one  turn  of  the 
coil  one  watt-hour  is 
registered  on  the  dial; 
but  this  is  such  a  small 
unit  that  it  cannot  be 
detected.  One  thousand 
turns  make  a  kilowatt- 
hour,  and  this  is  indi- 
cated by  1  on  the  first 
dial. 

The  reading  of  the  watt-hr.  meter  is  the  same  as  the 
gas-meter  (refer  to  gas-meter,  §69). 

At  the  bottom  of  the  meter  is  an  aluminum  disk  revolving 
between  permanent  magnets.  This  disk  acts  as  a  brake, 
so  that  the  coil  revolves  at  a  speed  proportional  to  the  watts 
used ;  it  also  stops  the  meter  when  the  current  is  turned  off ; 


FIGURE  194. — A  DIRECT  CURRENT  WATT- 
HOUR  METER  WITH  COVER  REMOVED. 


192      MOTION-PRODUCING  EFFECT  OF  CURRENT 


FIGURE  195.  —  AN  ALTERNATING 
CURRENT  WATT-HOUR  METER. 


very  small,  usually  not  over 


otherwise  the  coil  would 
coast  and  register  watt- 
hours  which  were  never 
used. 

Watch  your  meter  at 
home  speed  up  when  lights 
are  turned  on  and  slow 
down  when  they  are  turned 
off.  It  should  stop  when 
all  appliances  are  off;  and 
if  it  does  not,  have  it  re- 
ported, as  you  are  paying 
for  electricity  not  used. 
Be  sure  that  you  can  read 
your  meter,  and  then  check 
your  light  bills. 

226.   The  Starting-box.  - 

The  resistance  of  a  motor  is 

ohm.     If  it  were  attached 


directly  to  the  line,  as  is  shown  by  Figure  196,  the  coils  of 

the  motor  would  be  burned  out.     The  reason  for  this  is 

easily   seen.     If   the  voltage  is 

110  volts  and  the  resistance  is    ~liov~ 

J  ohm,   the   current  would    be 

110 


=  220  amperes,  which  would 


M 


FIGURE  196.  —  WIRING  DIAGRAM 
OF  A  MOTOR  DIRECTLY  ACROSS 
THE  LINE. 


burn  out  the  coils. 

In  order  to  protect  the  motor 

when  starting,  a  "  starting-box  "  is  used.  This  is  made  up 
of  coils  of  resistance  wire  placed  in  a  convenient  box,  so 
that  the  coils  may  be  cut  out  of  the  circuit  by  merely 
moving  a  handle  over  to  the  right.  (Figure  197.) 


C.   E.   M.   F. 


193 


FIGURE  197.  —  WIRING 
DIAGRAM  OF  A  SIMPLE 
STARTING-BOX. 


The  first  coil  begins  at  notch  No.  I  and  ends  at  No.  2. 
The  second  coil  starts  at  No.  2  and  ends  at  No.  3,  and  so  on. 
When  the  arm  is  on  No.  I  notch  the 
current  must  pass  through  all  five  coils. 
As  the  arm  is  moved  to  the  right,  coils 
are  cut  out. 

227.  C.  E.  M.  F.  —  It  is  easy  to  see 
why  the  starting-box  keeps  the  current 
small,  and  thus  protects  the  motor  while 
the  coils  are  all  in  the  circuit ;  but  it  is 
not  so  easy  to  see  why  the  current  does  not  get  large  when 
the  coils  are  cut  out. 

You  will  remember  that  we  said  that  whenever  lines  of 
force  are  cut  by  a  conductor  an  electric  pressure  is  generated. 
Now,  a  motor,  when  running,  has  loops  of  wire  (the  arma- 
ture) turning  in  a  mag- 
netic field  (field),  and 
thus  an  electric  pressure 
is  generated.  This  pres- 
sure is  in  the  opposite 
direction  to  the  applied 
pressure  or  E.  M.  F.,  and 
is  hence  called  counter- 
E.  M.  F.  or  C.  E.  M.  F. 
A  motor,  then,  when 
running,  generates  a 
C.  E.  M.  F.  which 
opposes  the  applied 
E.  M.  F.,  thus  neutraliz- 
ing part  of  it.  On  account  of  this,  the  coils  of  the  starting- 
box  may  be  cut  out,  as  the  C.  E.  M.  F.  holds  the  current 
down  when  the  motor  has  gotten  up  to  speed. 


FIGURE   198.  —  PHOTOGRAPH  OF  A  O-POINT 
STARTING-BOX. 


194      MOTION-PRODUCING  EFFECT  OF   CURRENT 


Suppose  the  motor  mentioned  above  generates  100  volts, 
C.  E.  M.  F.,  when  running  at  full  speed, 
110  -  100      10 


then 


=  —  =  20  amperes,  the  amount  of    current 


the  motor  would  take  when  running  at  full  speed. 


FIGURE  199.  —  PHOTOGRAPH  OF  A  4-poiNT 
STARTING-BOX. 

228.  Series  Motor.  —  There  are  three  general  classes  of 
D.  C.  motors :  Series,  Shunt,  and  Compound.  We  shall  dis- 
cuss only  the  first  two. 


IIOV 


r/WWWV ' 

Field  s — v. 
I       sf    \Arma1Lire 


FIGURE  200.  —  WIRING  DIAGRAM 
OF  A  SERIES  MOTOR  WITH 
STARTING-BOX  IN  THE  CIRCUIT. 


FIGURE  201.  —  WIRING  DIAGRAM  OF 
A  SHUNT  MOTOR  WITH  STARTING- 
BOX  CONNECTIONS. 


SHUNT  MOTOR 


195 


Figure  200  shows  the  connection  for  a  series  motor  with 
starting-box  in  the  circuit. 

The  term  series  is  used  because  the  armature  and  field 
are  connected  in  series.     The  starting-box  is  put  in  the  line, 
in  series  with  the  arma- 
ture and  field. 

The  speed  of  the 
series  motor  is  regulated 
by  putting  a  resistance 
in  series  with  the  motor. 
To  make  the  motor  run 
fast,  cut  out  resistance ; 
and  to  make  it  run 
slowly,  put  in  resistance. 
Why? 

Series  motors  are  used 
wrhere  the  motor  must 
start  under  load,  as  in 
the  case  of  a  street  car 
or  an  elevator.  Why? 

229.  Shunt  Motor.— 
The  term  shunt  is  used 
because  the  armature 
and  field  are  placed  in 
•"  shunt,"  or  parallel. 
Figure  201  shows  the  connections  of  a  shunt  motor  with 
starting-box  attached. 

The  current  comes  in  at  the  switch,  passes  to  the  point 
on  the  starting-box  marked  "  Line."  From  the  point 
marked  "  A  "  a  wire  leads  to  the  armature ;  and  from  the 
point  marked  "  F  "  a  wire  goes  to  the  field.  The  other 
ends  of  the  field  and  armature  are  connected  together, 


FIGURE  202.  —  VACUUM  CLEANER  DRIVEN 
BY  AN  ELECTRIC  MOTOR. 


196      MOTION-PRODUCING  EFFECT  OF  CURRENT 


FIGURE  203.  —  AN  ELECTRIC  FAN. 


and  then  attached  to  the 
other  side  of  the  line  at 
the  switch. 

Inside  of  the  starting- 
box,  a  wire  goes  from 
the  point  marked 
"  Line "  to  the  arm. 
From  the  last  notch  goes 
a  wire  to  the  point 
marked  "A"  and  from 
the  first  notch  goes  a 
wire  to  a  small  coil  C, 
and  then  to  the  point 
"  F." 

To  start  the  motor, 
close  the  switch;  then 

move  the  arm   of   the   starting-box   slowly  to    the    right, 

allowing    the    motor    to 

pick  up  speed. 

This  cuts  out  the  re- 
sistance in  the  armature 

circuit,  making  the  arma- 
ture turn  faster;   and  at 

the   same    time    it    puts 

resistance  into  the  field 

circuit,  which  also  makes 

the  armature  turn  faster. 

(Why?)     The  small  coil 

acts    as    a    magnet    and 

holds      the     arm      over 


When    it     is    pushed     far      FlGURE  204.- A  SMALL  ELECTRIC  MOTOR 
enough. 


USED  TO  DRIVE  A  SEWING  MACHINE. 


SHUNT  MOTOR 


197 


599 


FIGURE  205.  —  AN  ELECTRICAL  MOTOR  DESIGNED  TO  RUN  A 
WASHING  MACHINE. 

The  speed  is  regulated  by  putting  a  resistance  into  the 
field  circuit.  Putting  in  resist- 
ance makes  the  motor  speed  up. 
Taking  out  resistance  makes  it 
slow  down.  It  may  seem  unrea- 
sonable at  first  that  putting  in 
resistance  in  series  with  the  field 
of  a  shunt  motor  speeds  it  up, 
and  taking  out  resistance  slows  it 
down. 

The  reasons  for  these  charac- 
teristics are  readily  understood, 
however,  when  it  is  remembered 
that  the  thing  that  does  most  to 
control  the  current  through  a 
motor  is  the  C.  E.  M.  F.  which 
it  generates. 


FIGURE  206. — AN  ELECTRICAL 
MOTOR  ATTACHED  TO  A  WASH- 
ING MACHINE. 


198      MOTION-PRODUCING  EFFECT  OF  CURRENT 


FIGURE  207.  —  A  LARGE  A.  C.  POWER  MOTOR  DISASSEMBLED  TO  SHOW 
DIFFERENT  PARTS.     (SLIP  RING  TYPE.) 

The  armature  must  turn  fast  enough  to  generate  a 
C.  E.  M.  F.  almost  equal  to  the  applied  E.  M.  F.  If  the 
field  is  weak  the  armature  must  burn  fast,  but  if  it  is  strong 


FIGURE  208.  —  ANOTHER  LARGE  A.  C.  POWER  MOTOR  DISASSEMBLED. 
(SQUIRREL  CAGE  TYPE.) 


SPECIFIC    USES  OF  A.    C.   AND   D.   C.   MOTORS      199 

then  the  armature  need  only  turn  slowly,  to  generate  this 
necessary  C.  E.  M.  F. 

Therefore,  since  adding  resistance  in  series  with  the  field 
makes  the  field  weaker,  it  causes  the  motor  to  speed  up,  and 
since  taking  out  resistance  in  series  with  the  field  makes  the 
field  stronger,  it  causes  the  motor  to  slow  down. 

This  motor  is  used  where  it  can  start  without  load,  and 
can  then  have  the  load  thrown  on  gradually,  as  in  the  case 
of  motors  in  a  machine-room. 

230.  Small  Motors.  —  If  the  motor  is  small  enough,  it 
may  be  put  directly  on  the  line,  without  a  starting-box.     In 
this  case  the  armature  is  so  light  in  weight  that  it  can  start 
to  full  speed  before  the  coils  have  time  to  burn  out. 

231.  Specific  Uses  of  A.   C.  and  D.  C.  Motors  in  the 
Home.  —  Motors  for  either  A.  C.  or  D.  C.  circuits  are  often 
used  for  the  following  purposes : 

1.  Electric  fans.  4.   Kitchen  motors. 

2.  Sewing  machines.  5.   Vacuum  cleaners. 

3.  Washing  machines.  6.    Hair  driers. 

Name  any  other  uses  you  know. 


CHAPTER   XVIII 


INDUCTION 

232.  Permanent  Magnet  in  a  Coil  of  Wire.  —  Induction 
is  the  producing  of  an  electrical  pressure  (E.  M.  F.)  by  means 
of  a  conductor  cutting  magnetic  lines  of  force.  This  is  not  a 
new  idea,  but  is  one  which  we  have  been  using  all  through 

the  subject  of  Electricity. 
We  spoke  of  it  when  we 
studied  the  simple  generator. 
In  the  simple  generator 
the  conductor  moved  and 
cut  the  lines  of  force,  which 
remained  stationary.  This 
action  may  be  reversed,  — 
the  conductor  remaining 
stationary  and  the  field 
moving,  —  and  the  result 
will  be  the  same. 

Figure  209  shows  a  per- 
manent magnet  (M)  thrust  into  a  coil  of  wire  (C),  the  ends 
of  the  coil  being  connected  through  the  galvanometer  (G). 
When  this  is  done,  the  galvanometer  will  deflect,  showing 
that  a  current  passes  through  the  coil.  The  lines  of  force 
come  out  of  a  N-pole  and  go  around  and  into  a  S-pole. 
When  the  magnet  is  thrust  downward,  these  lines  are  cut 
by  the  wire  in  the  coil. 

200 


x^- 

'x- 

"N 

f      S** 

^^^ 

\  /  / 

Xy 

'; 

,.  ' 

'  — 

M 

r*v 

V 

'''    M 

1  1 

•»--- 
i 

fi 

, 
\ 
i 

1  1 

i 

I 

i 

1    1 

\\ 

i 

R 

|                  L^- 

\  \ 

j 

i, 

j^,.^*-^^** 

V*- 

\ 

rj 

y| 

P 

/' 

I 

"i 

/ 

. 

vv  a 

L  \ 

r.1-' 

\ 

I      ^ 

FIGURE  209.  —  A  PERMANENT  MAGNET 
BEING  THRUST  INTO  A  COIL  OF  WIRE. 


AN  ELECTRO-MAGNET  IN  A   COIL   OF   WIRE     201 


If  the  magnet  were  pulled  out,  the  lines  of  force  would 
be  cut  in  the  opposite  direction,  and  the  galvanometer  would 
deflect  in  the  opposite  direction,  showing  that  the  current  is 
reversed. 

Then,  to  thrust  a  N-pole  in  and  pull  it  out  immediately 
produces  an  A.  C.  current  in  the  coil. 

Just  the  reverse  action  takes  place  when  a  S-pole  is  thrust  in 
and  pulled  out,  since  the  lines  of  force  are  reversed.  That 
is,  to  pull  a  S-pole  out  is  the  same  as  to  thrust  a  N-pole  in, 
and  to  thrust  a  S-pole  in  is  the  same  as  to  pull  a  N-pole  out. 

233.  An  Electro-magnet  in  a  Coil  of  Wire.  —  Figure  209 
shows  a  coil  of  wire  with  a  permanent  magnet  thrust  into  it. 
Figure  210  shows  the 
same  coil  of  wire,  but 
instead  of  a  permanent 
magnet  an  electro- 
magnet has  been  used. 
The  effect  is  exactly 
the  same  as  before. 

Now,  if  instead  of 
thrusting  in  and  pull- 
ing out  this  electro- 
magnet, the  core  with 
the  wire  around  it  is 
placed  inside  the  coil 

of  wire,  and  the  key  (K)  is  pressed  and  released,  the  same 
effect  is  obtained. 

While  the  key  is  open,  the  core  is  not  a  magnet;  then 
when  it  is  pressed,  the  core  becomes  a  magnet,  giving  the 
same  effect  as  thrusting  a  magnet  in.  Again,  when  the 
key  is  released,  the  core  loses  its  magnetism,  and  the  result 
is  the  same  as  when  the  magnet  is  pulled  out. 


•:v      <• 

^_ 

i—  %z 
W 

P 

^ 

-— 

^ 
>    p 

^ 

1  AT 

FIGURE  210. — AN  ELECTRO-MAGNET  IN  A 
COIL  OF  WIRE. 


202 


INDUCTION 


Thus  we  see  that  if  two  coils  are  placed  so  that  one  is 
inside  the  other,  and  a  current  is  made  in  one,  a  current 
is  induced  in  the  other.  Also,  if  a  current  is  stopped  in 
one,  a  current  is  induced  in  the  other,  in  the  opposite 
direction. 

The  coil  in  which  the  current  is  made  or  stopped  is  called 
the  primary,  while  the  coil  in  which  the  current  is  induced 
is  called  the  secondary. 

234.  Mutual  and  Self-induction.  —  The  above  case  is 
called  mutual  induction.  It  is  the  producing  of  a  current  in 
one  wire  by  the  effect  of  a  current  in  another. 


FIGURE  211.  —  INDUCTION  APPARATUS. 

Self-induction  has  to  do  with  but  one  wire. 

It  takes  time  and  energy  to  start  an  automobile.  The 
tendency  of  the  automobile  to  hold  back,  or  stay  where  it 
is,  is  called  inertia.  The  tendency  for  a  current  not  to  flow 
ivhen  it  is  being  started,  and  to  keep  on  flowing  when  it  is  being 
stopped,  is  called  self-induction. 

Self-induction    always    takes    place    when    a    current    is 


THE  INDUCTION   COIL 


203 


changed  (made  larger  or  smaller)  in  a  circuit.     It  acts  in  the 
opposite  direction  to  the  change. 

235.  The  Induction  Coil.  —  The  induction  coil  or  "  spark- 
coil,"  is  used  to  increase  the  pressure  in  a  D.  C.  circuit  so 
that  a  spark  will  jump  across  a  gap. 

The  wiring  diagram  of  an  induction  coil  is  shown  in  Figure 
212. 

A  coil  of  heavy  wire  (p)  is  wound  on  a  soft  iron  core,  with 
a  few  turns.  Around  this  is  wound  a  coil  of  fine  wire,  with 
many  turns.  The  coil  of 
heavy  wire  is  called  the 
primary,  and  is  connected 
in  series  with  a  push 
button  (P),  a  battery  (£), 
and  a  vibrator  (F).  The 
fine-wire  coil  is  called  the 
secondary,  and  ends  at 
opposite  sides  of  a  spark 
gap.  A  condenser  (C)  is 
placed  across  the  gap 
made  by  the  vibrator. 

A  condenser  is  a  storage 
tank  for  electricity.  It  is  usually  made  up  of  layers  of 
tinfoil  insulated  from  one  another  by  mica  or  other  insulat- 
ing material,  alternate  layers  being  connected  together. 
Positive  electricity  flows  in  on  one  side,  and  negative  on 
the  other.  The  more  leaves  or  layers,  the  more  it  will  hold. 

In  the  primary  of  the  induction  coil  the  action  is  the  same 
as  in  the  door  bell,  the  vibrator  flying  backward  and  for- 
ward, making  and  breaking  the  current.  Whenever  the 
current  changes  in  the  primary,  a  current  is  induced  in  the 
secondary  by  mutual  induction. 


FIGURE  212.  —  WIRING  DIAGRAM  OF 
THE  INDUCTION  COIL. 


204  INDUCTION 

Since  there  are  several  times  as  many  turns  in  the  second- 
ary as  there  are  in  the  primary,  the  voltage  of  the  secondary 
will  be  just  that  many  times  as  great  as  in  the  primary. 

To  explain :  Suppose  the  primary  has  10  turns  and  the 
secondary  1000  turns,  and  that  the  primary  produces  a 
field  of  a  certain  strength.  Now,  for  every  turn  on  the 
primary  there  are  ™%^,  or  100,  turns  on  the  secondary. 
Hence,  the  secondary  cuts  100  times  as  many  lines  of  force 
as  the  primary.  Since  the  voltage  depends  upon  the  num- 
ber of  lines  cut  per  second,  the  voltage  in  the  secondary 
will  be  100  times  that  in  the  primary,  or 

voltage  of  secondary       turns  of  secondary 
voltage  of  primary          turns  of  primary 

Since  there  is  self-induction  wherever  a  current  is  started 
or  stopped,  the  making  and  breaking  of  the  primary  circuit 
is  not  accomplished  quickly.  The  condenser  is  put  in  over 
the  gap  to  make  this  action  take  place  more  quickly,  thus 
increasing  the  voltage  of  the  spark. 

236.  Uses  of  the  Induction  Coil.  —  The  induction  coil  is 
used  in  igniting  the  gas  in  gas  engines. 
It  is  also  used  for  medical  purposes. 
237.  The  Transformer.  —  The  in- 
duction coil  was  used  on  D.  C.,  the 
vibrator  changing  the  current  in  the 
primary.  Now  if  A.  C.  is  used,  a 
vibrator  need  not  be  put  in,  but  the 
primary  may  be  wound  about  a  soft 
iron  without  any  mechanism  to  regu- 
late it.  The  alternation  of  the 

FIGURE  213.— A  Low       current  takes  the  place  of  the  make 
VOLTAGE  TRANSFORMER.      and  break  of  the  induction  coil. 


THE   TRANSFORMER 


205 


Such  an  arrangement  is  called  &  transformer.     It  consists 
merely  of  two  coils  wound  on  a  soft  iron  core.     One  coil  is 
made  of  fine  wire  with  many  turns,  while  the  other  is  made 
of  heavy  wire  with  few 
turns. 

As  in  the  induction 
coil,  the  voltages  of  the 
coils  depend  upon  the 
ratio  of  the  number  of 
turns.  The  coil  which 
has  the  current  put  into 
it  is  called  the  primary, 
while  the  one  in  which 
the  pressure  is  induced 
is  called  the  secondary. 

The  commercial  trans- 
former has  four  coils ; 
two  with  fine  wire,  and 
two  with  coarse  wire, 
wound  on  the  same  com- 
mon core  of  laminated 
soft  iron.  The  ratio  of 
turns  in  these  coils  is 
10  to  1.  That  is,  for 
every  turn  on  a  coarse- 
wire  coil  there  are  10  turns  on  a  fine- wire  coil. 

By  connecting  the  coils  in  different  combinations  different 
voltages  may  be  obtained. 

With  a  110- volt  primary  line  six  voltages  may  be  obtained 
with  a  commercial  transformer  —  three  by  using  the  coarse- 
wire  coils  as  primary,  and  three  by  using  fine-wire  coils  as 
primary. 


FIGURE  214.  —  A  HIGH  TENSION 
(VOLTAGE'I  TRANSFORMER. 


206 


INDUCTION 


~y  I  Secondary 


FIGURE  2 1 5.  —  1  1 0  VOLTS 
TRANSFORMED  TO  2200  VOLTS. 


238.  Coarse-wire    Primary.  —  1.   If    the    primaries    are 
connected  in  parallel,  and  the  secondaries  in  series,  the  volt- 
age   will    be    ^  X  110  =  2200. 
(Figure  215.) 

2.  If  the  primaries  are  con- 
nected in  parallel  and  the  sec- 
ondaries in  parallel,  the  voltage 
will  be  ^  X  1 10  =  1 100.  (Figure 
216.) 

3.  If  the  primaries  are  connected  in  series  and  the 
secondaries  in  parallel,  the  voltage  will  bo  V  X  110  =  550. 
(Figure  217.) 

239.  Fine-wire  Primary.  —  1.    If  the  primaries  are  con- 
nected in  parallel  and  the  second- 
aries in  series,  the  voltage  will  be 

AX  HO  =  22.     (Figure  218.) 

2.  If   the  primaries  are  con- 
nected in  parallel  and  the  second- 
aries in  parallel,  the  voltage  will 
be  A  X  110  =  11.     (Figure  219.) 

3.  If    the   primaries   are    connected    in    series    and    the 
secondaries  in  parallel,  the  voltage  will  be  ^  X  110  =  5^. 
(Figure  220.) 

240.  Uses  and  Advantages  of  the 
Transformer.  —  First  of  all,  you 
must  remember  that  transformers 
can  be  used  only  on  A.  C. 

They  are  used   for  stepping  the 
voltage  up  or  down.     Your   house 
circuit   is  not  in  electrical  connec- 
tion with  the  power  station,  but  comes  from  a  transformer 
near  the  house,  where  the  voltage  has  been  stepped  down 


nmar 
IIOV 

±_ 

\               ,  , 

Secondanj 

./  ./  JJJ 

IIOOV 

C  C 

i  I  1 

FIGURE  216. —  110  VOLTS 
TRANSFORMED  TO   1100  VOLTS. 


; 

550 

IIOV 


FIGURE  217.— 110  VOLTS 
TRANSFORMED  TO  550 
VOLTS. 


USES  AND   ADVANTAGES  OF   TRANSFORMER     207 


nabry 
22V 

1 

i  Z~~S 

Primary 

f  i  i  /  ii 

d 

HOV 

r  /• 

-1'! 

FIGURE  218.  —  110  VOLTS  TRANS- 
FORMED TO  22  VOLTS. 


from  2300  volts  to  110  volts.  In  fact,  wherever  power 
is  to  be  delivered  some  distance  it  is  sent  out  at  high 
voltage,  and  then  stepped  down  so  that  it  can  be  used. 

The  transformer  has  many 
advantages,  but  the  four  prin- 
cipal ones  are  these : 

1.  It  makes  it  possible  to  get 
any  voltage  you   like  from   any 
voltage  delivered. 

2.  It  saves  cost  of  wire.    Since 

power  =  E  •  I,  if  the  power  is  sent  out  at  a  large  volt- 
age, the  current  may  be  small,  and  since  it  is  the  current 

that  heats  a  wire,  the  wire  may 
be  small  wrhen  the  current  is 
small. 

3.  It  saves  line  drop,  or  fall  of 
voltage.  The  fall  of  voltage  along 
a  line  is  the  resistance  of  the  line 
X  the  current  flowing.  We  saw 
how  the  current  could  be  made 

smaller  with  the  transformer,  and  so  line  drop  is  cut  down. 
4.    It  saves  line  loss.     Line  loss  is  power  lost  in  the  line, 
and  is  the  line  drop  X  current.     Since  the  transformer  makes 
it  possible  to  reduce  both  the  line 
drop  and  the  current,  it  makes 
it  possible  to  reduce  the  line  loss. 
On  account  of  the  advantages 
just  named  nearly  all  transmis- 
sion   lines   are   of   high    tension 
(voltage) .    Being  of  high  voltage, 
they  are  dangerous,  and  so  are  usually  put  up  on  strong 
towers,  very  well  insulated,  the  wires  themselves  being  bare. 


.  (  — 

Primary 

JJJ  J  \  )  ) 

= 

IIV 

- 

MOV 

/ 

FIGURE  219.— 110  VOLTS 
TRANSFORMED  TO   1 1  VOLTS. 


condaru 

s£v 

p 

i 

Prirvrtf 

- 

10V 

r  r 

'  -| 

FIGURE  220.— 110  VOLTS 
TRANSFORMED  TO  5|  VOLTS. 


208 


INDUCTION 


241.   The   Three-phase    System.  —  Heretofore   we   have 
always  considered  an  electric  circuit  as  having  two  lines,  one 
line  out  and  one  line  back. 

The  modern  system  of  delivery  is 
what  is  called  the  "  three-phase " 
system.  It  consists  of  three  wires  in- 
stead of  two,  and  carries  three  times  as 
much  power  as  a  two-line  system. 

The  generator  for  three-phase  current 
is  so  arranged  that  the  current  goes  out 
on  one  of  the  wires  and  comes  back  on 
the  other  two,  or  goes  out  on  two  and  comes  back  on  one. 

For  example,  at  one  instant  the  current  is  flowing  out  on 
line  No.  1  (Figure  221),  and  at  the  same  time  is  coming  back 

Sub-Station 
Transformer 

'  2 


FIGURE  221.  — WIRING 
DIAGRAM  OF  A  3- 
PHASE  GENERATOR. 


Generator 


on  poles 


FIGURE  222.  —  WIRING  DIAGRAM  OF  A  S-PHASE 
CITY  SYSTEM. 


on  No.  2  and  ATo.  3  ;  an  instant  later  it  will  go  out  on  No.  2, 
and  come  back  on  No.  1  and  No.  3,  etc. 

This  is  the  system  used  in  Cleveland,  Ohio,  by  the  Illu- 
minating Company. 


WIRING  DIAGRAM   OF  HOUSE   CIRCUIT 


209 


242.  The  Wiring  Diagram  of  a  City  System.  —  Figure  222 
shows  the  general  wiring  diagram  of  a  city  using  a  3-phase 
current.  The  elec- 

n 


3 


tricity  is  generated 
at  the  generator  (G) 
at  11,000  volts,  and 
is  sent  out  to  the 
sub-stations  (S)  in 
conduits  under 
ground.  Here  it 
runs  through  trans- 
formers and  is 
stepped  down  to 
2300  volts.  This  is 
carried  out  on  poles 
to  the  locality  in 
which  it  is  to  be  used. 
Here  it  is  stepped  down  to  110  volts  by  transformers  placed 
on  the  poles.  This  110-volt  line  is  carried  into  the  houses. 
243.  Wiring  Diagram  of  House  Circuit.  —  The  current  is 
brought  into  the  house  on  two  insulated  wires  at  110  volts. 


FIGURE  223.  —  WIRING  DIAGRAM  OF  A  HOUSE 
CIRCUIT. 


B  B 

FIGURE  224. — WIRING  DIAGRAM  OF  A  SIMPLE  TELEPHONE  CIRCUIT. 


210 


INDUCTION 


A  city  ordinance  usually  requires  that  all  new  wiring  must 

enter  the  house  at  the  basement.     Just  after  it  enters  the 

^^^      house  it  passes  through  fuses.     (Fi,  Figure 

off      223.)     Then    it    goes    through    the    service 

^     f          switch  (S)  to  the  meter  (M) ;  then  through 

Br^ff  another  set  of  fuses  (Fz) ;  and  then  to  the 

t  \       "•  fixtures  in  the  house ;  all  the  appliances  being 

^^^^^      put  in  parallel,  across  the  line. 

4feS§^          244.   The  Telephone. — The  telephone  uses 

FIGURE  225.  —  A 
PORTABLE  TELE- 
PHONE RECEIVER 
AND  TRANS- 

M1TTER. 

the  principle  of 
the  transformer. 
Figure  224  shows 
a  diagram  of  the 
simple  Bell  tele- 
phone. 

In  the  trans- 
mitter is  a  layer 
of  powdered  car- 
bon (C)  between 
two  plates  ( P  and 
P).  By  this  ar- 
rangement an 
electric  circuit  is 

established,  pass-   FIGURE    226  —  A    DESK    TELEPHONE    SWITCHBOARD 
^i  i      ,1  •  SUCH  AS  is  USED  AS  A  LOCAL   SWITCHBOARD  BY 

mg  through   this        A  LARGE  BUSINESS  CONCERN. 

carbon  to  a  bat- 
tery (B),  and  through  the  primary  of  the  transformer  (T). 
The  secondary  circuit  consists  of  the  following  parts,  all 


THE   TELEPHONE  211 

being  put  in  series  :  (a)  the  secondary  coil  of  the  local  trans- 
former, (b)  the  secondary  coil  of  the  transformer  at  the 
other  station,  (c)  the  coil  of  wire  about  the  permanent 
magnet  at  the  local  station,  (d)  the  similar  coil  about  the 
permanent  magnet  at  the  other  station,  and  (e)  the  connect- 
ing line  wires. 

When  the  speaker  talks  into  the  transmitter,  the  little 
plate  P  alternately  squeezes  and  releases  the  carbon,  thus 
reducing  and  increasing  its  resistance.  This  causes  the  cur- 
rent in  the  primary  to  fluctuate.  This  induces  an  alternat- 
ing current  in  the  secondary,  which  in  turn  strengthens  and 
weakens  the  permanent  horseshoe  magnets.  As  these  mag- 
nets are  strengthened  and  weakened,  they  first  pull,  and 
then  release,  the  steel  plate  (P2)  in  the  receiver,  causing  it  to 
flip  backward  and  forward.  This  plate  (P2)  then  reproduces 
the  sound  that  enters  the  transmitter. 


CHAPTER   XIX 
CHEMICAL  RELATION   OF    AN  ELECTRICAL    CURRENT 

245.  The  Electrolytic  Cell.  —  Sometimes  liquids  instead  of 
solids  are  used  as  conductors  of  electricity.     For  instance,  a 
salt  solution  will  conduct  electricity.     When  the  current 
passes  through  a  solution  like  this,  a  chemical  change  takes 
place  which  is  quite  different  from  what  happens  when  a 
substance  like  mercury  conducts  electricity. 

The  solution,  with  the  points  of  contact,  is  called  an 
electrolytic  cell. 

246.  Chemical  Action  in  an  Electrolytic  Cell.  —  When  a 
solution  is  made,  part  of  its  molecules  break  up  into  parts 
or  ions,  and  are  said  to  ionize.     Before  this  can  be  under- 
stood a  few  terms  must  be  learned. 

An  atom  is  the  smallest  known  part  of  an  element  which 
will  enter  into  a  chemical  change.  For  example,  a  copper 
atom  is  the  smallest  known  part  of  the  element  copper 
which  will  enter  into  a  chemical  change.  We  let  the 
symbol  Cu  stand  for  it. 

A  radical  is  a  group  of  atoms  acting  as  a  single  atom  in 
a  given  chemical  change.  For  example,  in  CuSO±  the  SO^ 
is  called  a  radical,  and  does  not  break  up  in  a  given  chem- 
ical change. 

An  ion  is  an  atom  or  a  radical,  with  an  electrical  charge. 
For  example,  a  Cu  atom  with  a  charge  of  electricity  is  called 
a  copper  ion,  and  is  written  Cu+.  Also,  the  radical  S0± 

212 


THE  ELECTROLYTIC   CELL 


213 


with  a  charge  of  electricity  becomes  an  ion,  and  is  called  a 
sulphate  ion  and  is  written  S04~~.  Positive  ions  carry  posi- 
tive charges,  and  negative  ions  carry  negative  charges.  The 
same  kind  of  atoms  or  radicals  always  carry  the  same  kind 
of  charge. 

Thus,  when  we  say  a  solution  ionizes;  we  mean  it  breaks 
up  into  atoms  and  radicals  carrying  electrical  charges. 

When  an  electrical  current  passes  through  a  solution,  the 
positive  ions  are  made  to  flow  with  the  current,  while  the 
negative  ions  flow  in  the  other  direction.  Also,  more  of 
the  solution  ionizes.  This  is  the  way  a  solution  conducts  the 
current. 

247.  Parts  of  an  Electrolytic   Cell.  —  The  parts   of  an 
electrolytic  cell  are  (1)  the  solution,  which  is  called  the  elec- 
trolyte; (2)  the  contact,  or  pole  where  the  current  comes  in, 
called   the  anode;    and  (3)   the  contact,  or  pole  where  the 
current  goes  out,  called  the  cathode. 

248.  The  Copper  Sulphate  (CuSO4)  Electrolytic  Cell.  — 
A  solution  of  CuSo^  with  a  copper  anode  and  any  other 
conductor  for  a  cathode,  will 

make  an  electrolytic  cell. 
(Figure  227.)  The  action  is 
as  follows : 

When  the  current  is  turned 
on,  the  CuSot  ionizes  (some  of 
it  is  already  ionized)  into  Cu+ 
and  $04~.  The  Cu+  passes 
over  to  the  cathode  and  gives 
up  its  charge,  and  places  the 
Cu  on  the  cathode.  The  *S04 
passes  over  to  the  anode,  unites  with  an  atom  of  the  copper 
plate,  —  with  the  aid  of  the  positive  charge  coming  through 


Cu. 


FIGURE  227.  —  A  COPPER  SUL- 
PHATE ELECTROLYTIC  CELL. 


214 


CHEMICAL   RELATION   OF   CURRENT 


the  wire,  —  and  forms  new  CuS04.  As  this  action  contin- 
ues, the  cathode  becomes  plated  with  copper,  and  the 
anode  is  eaten  away. 

This   action   can   be   expressed   by   the   three    following 
equations  : 


Cu+  +  S04- 

Cu+      -+•  Cu   +  (  + 

so,-  +  Cu  +  (  +  )  — 

249.   The  Sulphuric  Acid  (H2SO4)  Electrolytic  Cell.  -     A 
solution  of  HzSO*  with  a  cathode  and  anode  of  platinum 

will   form   an   electrolytic 
cell.    (Figure  228.) 

The  action  is  as  follows  : 
The  HzSOi  ionizes  into 
ndS04~.   The2#2+ 
I     sl__  ____   H  "  passes  over  to  the  cathode 

and  there  deposits  its 
charge,  the  free  hydrogen 
bubbling  off  as  a  gas. 
The  S04~  passes  over  to 
the  anode,  but  cannot 
attack  the  platinum,  so 
it  unites  with  a  molecule 
of  water  (H20),  with  the 
aid  of  the  positive  charge 

(  +  )  coming  through  the  wire,  and  forms  a  new  mole- 
cule of  H2SOt,  the  remaining  oxygen  bubbling  off  as  a 
gas.  As  this  action  continues,  the  two  plates  remain  the 
same,  but  the  solution  becomes  concentrated,  as  H-0  is 
taken  off  in  its  two  constituent  gases. 

This  action  may  be  expressed  by  the  three  following 
equations  : 


FIGURE  228.  —  A  SULPHURIC  ACID 
ELECTROLYTIC  CELL. 


ELECTRO-TYPING  215 


SO,'  +  H20  +  (  +  )  —  >-  H,SO*  +  0 

There  are  many  different  electrolytic  cells  but  the  action 
in  all  is  similar  to  that  in  the  two  just  studied. 

250.  Electro-plating.  —  The   electrolytic    cell   is  used  in 
plating.     A  solution  containing  a  salt  of  the  metal  to  be 
plated  on  the  object  is  used  as  an  electrolyte.     The  object  to 
be  plated  is  used  as  a  cathode,  and  the  anode  is  of  the  same 
material  as  the  metal  to  be  plated  on  the  object.      The 
action  is  exactly  the  same  as   in   the   case   studied   under 
the  CuSOt  electrolytic  cell. 

Many  precautions  are  required  to  make  plating  success- 
ful. The  solution  must  be  of  just  the  right  strength,  the 
object  to  be  plated  must  be  perfectly  clean,  and  the  rate 
of  plating,  or  the  size  of  the  plating  current,  must  be  just 
right. 

It  is  by  this  process  that  nearly  all  modern  plating  is  done. 
Name  some  things  that  are  silver-plated.  Some  that  are 
nickel-plated,  some  that  are  gold-plated. 

251.  Electro-typing.  —  Electro-typing  is  another  of  the 
useful  things  done  by  means  of  the  electrolytic  cell.     All 
the  cuts  in  books,  magazines,  and  newspapers  as  well  as  the 
reading  matter  of  most  of  our  books  are  made  by  electro- 
typing.     (The  reading  matter  of  most  newspapers  is  not 
electro-typed.) 

If  the  thing  to  be  electrotyped  is  a  page  of  printed  matter, 
the  type  is  first  set  up.  Then  an  impression  is  made  in  wax. 
This  impression  is  next  sprinkled  with  graphite  to  make  it 
a  smooth  conducting  surface.  Then  this  form  is  used  as  the 
cathode  in  a  plating  cell.  Copper  about  the  thickness  of 


216  CHEMICAL  RELATION  OF  CURRENT 

paper  is  plated  on  the  graphite  surface.  This  is  then  backed 
with  type-metal  to  make  it  strong,  and  the  wax  is  melted 
off.  This  plate  can  then  be  used  as  often  as  desired,  and  is 
easily  stored  away.  The  type  used  at  the  beginning  can 
be  used  over  and  over  again. 


CHAPTER  XX 
BATTERIES 

252.  The  Simple  Voltaic  Cell.  —  We  have  learned  that 
an  electrical  pressure  is  generated  whenever  lines  of  force 
are  cut  by  a  conductor.     Here  are  three  other  known  ways 
by  which  an  electrical  pressure  may  be  produced : 

1.  By  chemical  action. 

2.  By  certain  kinds  of  friction. 

3.  By  heating  two  metals  in  contact. 

If  a  glass  jar  has  a  solution  of  common  salt  put  into  it, 
and  a  zinc  strip  and  copper  strip  be  put  into  the  solution 
and  joined  together  by  a  conductor,  an  electrical  current 
will  flow.  The  jar  of  salt  water  with  its  copper  and  zinc 
strips  is  called  a  voltaic  cell,  for  it  generates  an  electrical  pres- 
sure. The  pressure  is  set  up  by  the  chemical  action  which 
takes  place  in  the  cell. 

Care  should  be  taken  not  to  confuse  the  terms  "  voltaic 
cell  "  and  "  electrolytic  cell."  The  latter  is  merely  a  con- 
ductor  of  electricity,  while  the  former  produces  an  electrical 
pressure. 

253.  The  H2SO4  Voltaic  Cell.  —  There  are  several  kinds 
of   voltaic   cells.     We   just   learned   that   salt   water   with 
copper  and  zinc  strips  for  "  electrodes  "  forms  a  voltaic  cell. 
So,  also,  does  dilute  H^SO*  with  copper  and  zinc  electrodes. 

Let  us  note  the  chemical  action  that  takes  place  in  the 
H2SO,  voltaic  cell.  (Figure  229.) 

217 


218 


BATTERIES 


As  soon  as  the  circuit  is  closed,  the  ionized   HiSOi  sepa- 
rates, the  H2  going  to  the   Cu  electrode  and  giving  up  its 

charge,  the  2  H  being  given 
off  as  a  gas.  The  S04  goes 
to  the  Zn  plate,  receives  the 
positive  charge  coming  around 
the  wire,  and  unites  with  the 
Zn  to  form  ZnSO±  (zinc  sul- 
phate). 

This  action  may  be  shown  by 
the  three  following  equations : 

Hf      — >-  2  H  +  (  +  ) 
SOt-  +  Zn  +  (+)  — >•  ZnSO* 

FIGURE  229.  —  A  SULPHURIC  ACID         „, 

VOLTAIC  CELL.  Ihus  we  see  that  an   elec- 

trical current  is  sent  through 

the  wire,  that  the  HzSO^  is  used  up,  that  ZnSO*  is  made  in 
its  place,  and  that  the  Zn  strip  is  eaten  up. 

254.  Polarization.  —  It  was  seen  above  that  hydrogen  gas 
is  given  off  at  the  copper  plate.     In  all  cells  where  this  is 
done  there  is  a  tendency  for  these  hydrogen  bubbles  to  stick 
to  the  plate,  and  thus  insulate  it.     This  is  called  polarization. 

255.  Open-circuit  Cells.  —  Cells  which  polarize    cannot 
be  run  for  long  periods,  because  the  positive  plate  becomes 
insulated  by  the  hydrogen.     Therefore  these  cells  are  called 
"  open-circuit  cells,"  because  the  circuit  on  which  they  are 
placed  must  remain  open  most  of  the  time  and  can  be  closed 
for  only  short  periods. 

Name  some  uses  of  open-circuit  cells. 

256.  The  Wet  Salammoniac  Cell.  —  An  open-circuit  cell 
may  be  made  by  placing  a  handful  of  ammonium  chloride 


THE  ADDWATER   CELL 


219 


Zn 
NH.CI 

MnO, 


FIGURE  230.-  CROSS 

SECTION  OF  A  SIMPLE 

DRY  CELL. 


in  a  quart  jar  filled  with  water,  using  a  strip  of 
carbon  for  a  positive  electrode  and  a  zinc  strip  for  a  nega- 
tive electrode.     This  cell   is  often  used 
for  doorbells. 

257.  The  Dry  Cell.  —  The  dry  cell 
has  the  same  chemical  action  as  the  wet 
NH4Cl  cell,  but  it  is  constructed  differ- 
ently, so  that  it  may  be  handled  much 
easier. 

Figure  230  shows  a  cross   section  of 
this  cell.     The  outside,  or  case,  is  zinc, 
and  acts  as  the  negative  electrode.     The 
center  portion  (C)  is  a  stick  of  carbon,  which  is  the  positive 
electrode.     Packed  in  around  this  carbon  stick  is  a  paste  of 
NH4Cl  and  manganese  dioxide  (MriOz).     The  NH^Cl  is  the 
active  portion,  and   the   manganese  dioxide   is   put   in  to 

retard    polarization.     This    is   an 
open-circuit  cell. 

The  top  shaded  portion  is  tar, 
or  wax,  used  to  seal  the  cell  so 
that  the  moisture  will  not  dry  out. 
This  cell  gives  about  1.4  volts, 
and,  when  new,  will  give  as  high 
as  30  amperes  on  short  circuit. 
Name  some  uses  of  the  dry  cell. 
258.  The  Addwater  Cell. - 
The  Addwater  cell  is  an  open- 
circuit  cell,  the  construction  of 
which  is  kept  secret  by  the  manu- 
facturers. Its  advantage  over  the 
ordinary  dry  cell  is  the  fact  it  will  last  longer,  as  it  has  a 
well  to  be  filled  with  water,  thus  keeping  it  from  drying  out. 


COP 


Knur/  Hut 
Acorn  Head  Post 


Carbon  E/ec/rode 


-  Pu/pboord  Bottom 


FIGURE  231.  —  CROSS  SECTION 
OF  A  COMMERCIAL  DRY  CELL, 
AS  IT  is  NOW  MANUFACTURED. 


220 


BATTERIES 


259.  Closed-circuit  Cells.  —  In  the  case  of  some  voltaic 
cells  there  is  no  hydrogen  given  off  in  the  form  of  a  gas,  and 
so  these  cells  do  not  polarize.  Keeping  the  circuit  closed 
for  a  long  period  does  not  harm  them, 
and  they  are  called  "  closed-circuit 
cells." 

Name  some  uses  for  closed-circuit 
cells. 

260.  The  Gravity  Cell.  —  The  gravity 
cell  consists  of  two  solutions  placed  in  a 
glass  jar  with  copper  and  zinc  electrodes. 
These  two  solutions  are  concentrated 
CuSO*  and  dilute  ZnSO*  (5-1 ) .  The  CuSO* 
is  placed  in  the  bottom,  and  the  ZnSO^  on 
top.  They  keep  these  relative  positions 
on  account  of  their  difference  in  density, 
hence  the  name  "  gravity  cell." 

The  copper  plate  is  placed  in  the  CuSO*, 
and  the  zinc  plate,  or  "  crowfoot,"  is  hung 
in  the  ZtiSO*.  The  circuit  must  be  kept 
closed,  or  the  two  liquids  will  diffuse,  thus 
These  cells  are  used  on  telegraph  lines. 

261.  The  Daniell  Cell.  —  The  Daniell  cell  is  similar  to  the 
gravity  cell,  except  that  the  ZnSO*  is  placed  in  a  clay  porous 
cup  so  that  the  cell  may  be  handled  without  danger  of  mix- 
ing the  solutions.     The  action  is  exactly  the  same  as  in  the 
gravity  cell. 

262.  Secondary  or  Storage-cells.  —  The  voltaic  cells  we 
have  been  studying  are  capable  of  giving  an  electrical  pres- 
sure as  soon  as  they  are  set  up,  and  are  therefore  called 
primary  cells.     It  has  been  found  that  cells  may  be  made 
which  will  not  at  first  give  an  electrical  pressure,  but  which 


FIGURE  232. — THE 
ADDWATER  CELL, 
WHICH  is  A  SPECIAL 
KIND  OF  DRY 
CELL. 


spoiling  the  cell. 


THE  LEAD    WET  STORAGE-CELL 


221 


will  do  so  if  "  charged."      These  cells  are  called  "  second- 
ary cells  "  or  "  storage-cells" 

263.  The  Lead  Wet  Storage-cell.  —  A  storage-cell  may 
be  made  by  using  two  lead  plates  for  electrodes  and  dilute 
H<iS04  for  an  electrolyte. 
(Figure  233.) 

When  first  set  up,  this 
cell  will  not  give  a  pres- 
sure, but  if  a  D.  C.  current 
is  allowed  to  flow  through 
it  for  a  time  it  is  said  to 
become  "  charged,"  and 
will  then  give  an  electrical 
pressure. 

The  charging  current 
causes  a  chemical  action 

to  take  place  within  the  cell,  thus  storing  up  chemical 
energy.  No  electricity  is  stored  in  the  cell.  Then,  when 
the  cell  is  used  to  give 
pressure,  the  current 
flows  in  the  opposite  di- 
rection, at  the  expense  of 
the  chemical  energy  stored 


FIGURE  233.  —  A  DIAGRAM  OF  A  WET 
LEAD  STORAGE  BATTERY. 


Source  of 
Pressure 


FIGURE  234. --WIRING  DIA- 
GRAM OF  A  STORAGE  BATTERY 
CHARGING  CIRCUIT. 


FIGURE  235. —  A  COMMERCIAL  LEAD 
STORAGE  BATTERY. 


in  it.     When  this  energy  is  exhausted,  the  cell  must  be 
recharged. 


222  BATTERIES 

To  charge  the  cell,  a  D.  C.  must  be  used,  and  the  +  pole 
of  the  charging  circuit  must  be  connected  to  the  +  pole  of 
the  cell.  (Figure  234.) 

If  A.  C.  is  used,  it  must  first  be  rectified,  that  is,  changed 
into  D.  C.  by  a  motor  generator,  a  rotary  converter,  or  a 
mercury  vapor  lamp. 

The  lead  storage-cell  is  easily  injured,  so  a  few  precau- 
tions may  be  appropriately  named : 

1.  D.  C.  current  must  be  used  for  charging. 

2.  Do  not  overcharge. 

3.  Do  not  short  circuit. 

4.  Do  not  charge  too  fast. 

5.  Do  not  let  it  remain  uncharged. 

6.  Keep  it  filled  with  pure  water. 

The  lead  storage  battery  is  used  for  many  things.  Some 
of  these  uses  are : 

1.  To  run  electric  motor  cars. 

2.  To  start  motors  and  to  light  cars. 

3.  To  light  houses  in  the  country. 

4.  For  plating. 

The  lead  storage-cell  gives  about  2  volts  per  cell,  regardless 
of  the  size  of  the  cell. 

264.  The  Dry  Lead  Storage-cell.  —  There  has  just  re- 
cently been  put  on  the  market  a  dry  lead  storage-cell 
(Figure  236),  but  as  yet,  its  success 
has  not  been  shown.  It  may,  or  may 
not,  be  good.  Its  principle  is  ex- 
actly the  same  as  the  wet  lead  cell, 
but  instead  of  the  acid  being  in  a 
free  state,  it  is  absorbed  by  a  com- 

FIGURE  236.  —  DIAGRAM  OF  ,     ,,          «  <   S      ,,        n 

A    DRY    LEAD     STORAGE    Pound>  thus   forming  a       dry       cell. 
BATTERY.  The  electrodes  are  lead  plates  wound 


THE  EDISON  STORAGE-CELL 


223 


in  concentric  spirals,  thus  giving  a  large  active  area.  The  ab- 
sorbing compound  is  pressed  in  between  the  plates  with  such 
force  that  the  active  material  on  the  plates  cannot  come  out. 

If  this  cell  proves  to  be  good,  it  will  be  a  great  step  in 
storage  battery  construction,  for  free  acid  is  a  dangerous 
thing  to  handle. 

265.  The  Edi- 
son Storage-cell. 
-Thomas  A.  Edi- 
son has  had  an 


QSlTIVC  POLE 


FIGURE  238.  —  THE 
POSITIVE  AND  NEGA- 
TIVE PLATES  OF  AN 
EDISON  CELL. 


FIGURE  237.  —  DISSECTED  VIEW  OF.  AN  EDISON 
STORAGE  BATTERY  CELL. 


altogether  different  storage-cell  on  the  market  for  some 
time.  This  cell  has  potassium  hydroxide  (KOH}  for  an 
electrolyte,  and  patented  nickel  and  steel  electrodes.  The 
container  is  a  pressed-steel  box,  so  that  it  is  almost  in- 
destructible. The  Edison  cell  does  not  need  the  care 
that  a  lead  cell  does,  and  can  be  subjected  to  much  more 


224  BATTERIES 

rough  handling,  without  injury.     A  short  circuit  does  not 
permanently  harm  it,  if  it  is  immediately  recharged. 


FIGURE  239. —  A  WOODEN  TRAY  CONTAINING 
5  EDISON  CELLS. 

The  voltage  of  the  Edison  storage-cell  is  lower  than  that 
of  the  lead  cell,  it  being  about  1.5  volts;  and  its  efficiency 
runs  lower  than  the  lead  cells. 

STATIC   ELECTRICITY 

266.  Static  Electricity.  —  Till  now  we  have  been  study- 
ing about  dynamic  or  current  electricity.  But  there  is 
another  kind  called  static  electricity. 

There  are  many  applications  of  this  form  of  electricity, 
such  as  lightning,  wireless  telegraphy,  and  medical  uses. 
When  we  scuff  across  a  thick  rug  in  a  cold  room  and  then 
touch  a  metal  door-knob  or  gas-fixture,  we  get  a  slight  shock 
due  to  static  electricity. 

Although  the  applications  of  static  electricity  are  spectac- 
ular and  interesting,  it  has  not  the  widespread  practical 


STATIC  ELECTRICITY 


225 


FIGURE  240. — AN  ACTUAL  PHOTOGRAPH  OF  A  STROKE  OF  LIGHTNING 
TAKEN  ON  THE  SHORE  OF  LAKE  MICHIGAN. 

value  of  current  electricity.     For  this  reason  a  complete 
treatment  of  it  is  not  embodied  in  this  book. 

Review  Problems 

1.  Discuss  the  field  about  a  magnet. 

2.  Distinguish  between  a  magnetized  piece  of  iron  and  one  which 
is  not  magnetized. 

3.  Why  is  magnetism  studied  before  electricity  ? 

4.  How  may  an  electrical  pressure  be  generated?     What  deter- 
mines its  amount  and  its  direction? 

5.  Discuss  pressure,  current,  and  resistance. 

6.  Distinguish  between  A.  C.  and  D.  C. 

7.  How  is  an  A.  C.  made  D.  C.  ? 

8.  Describe  the  space  about  a  wire  carrying  a  current. 

9.  What  determines  the  poles  of  an  electro-magnet? 

10.  Name  ten  applications  of  the  electro-magnet. 

11.  How  does  electricity  produce  heat? 


226  BATTERIES 

12.  Name  five  electrical  quantities  to  be  measured,  the  unit  used  for 
each,  and  the  letter  used  to  denote  each. 

13.  If  a  door  bell  has  180  ohms  resistance,  what  current  will  it  take 
if  6  volts  are  applied  to  it  ? 

14.  What  is  the  cost  of  running  a  motor  for  2  hours,  if  it  takes  3 
amperes  on  1 10  volts,  the  cost  of  electricity  being  9^  per  Kw.-hr.  ? 

15.  How  long  would  a  starting-battery  last  if  it  contained  600  watt- 
hours  and  gave  a  pressure  of  6  volts  at  a  300-ampere  discharging  rate? 

16.  Compare  the  cost  of  running  four  25-watt  lamps  to  that  of  three 
40-watt  lamps. 

17.  How  much  would  you  save  on  your  electricity  bill  if  you  had  an 
attachment  like  the  "  dim-a-lite,"  which  would  throw  in  an  additional 
100  ohms  to  the  340  ohms  if  the  lamp  were  to  burn  8  hours  on  a  110- 
volt  circuit,  and  cost  9^  per  Kw.-hr.? 

18.  In  problem  17  would  the  lamp  be  as  bright  with  the  extra  100 
ohms  in  the  circuit? 

19.  What  heats  an  electrical  flat-iron? 

20.  How  does  electricity  produce  motion? 

21.  Explain  how  the  ammeter  measures  current. 

22.  Show  where  a  voltmeter  and  an  ammeter  should  go  in  a  circuit. 

23.  What  is  the  difference  between  A.  C.  and  D.  C.  meters? 

24.  Discuss  the  essential  parts  of  a  watt-hour  meter. 
26.   What  is  C.  E.  M.  R? 

26.  Tell  briefly  the  difference  between  a  series  and  a  shunt  motor. 

27.  What  is  induction  ? 

28.  Discuss  mutual-  and  self-induction. 

29.  How  could  you  get  6  volts  from  a  120-volt  A.  C.  line? 

30.  If  the  two  coils  of  a  transformer  have  their  turns  in  the  ratio  of 
3  and  24,  what  voltages  could  you  get  from  a  110-volt  A.  C.  line? 

31.  What  is  the  advantage  of  the  3-phase  system? 

32.  Discuss  the  wiring  diagram  of  a  house. 

33.  What  is  the  difference  between  an  electrolytic  cell  and  a  voltaic 
cell? 

34.  Explain  how  silverware  is  plated. 

35.  Why  is  a  dry-cell  called  an  "  open-circuit  cell  "? 

36.  Give  some  applications  of  static  electricity. 


CHAPTER   XXI 
MECHANICS    OF    SOLIDS 

267.  Units  of  Measurement.  —  The  things  with  which 
physics  deals  are  very  definite,  and  so  require  definite  units 
to  measure  them.     For  example,  the  houses  we  live  in  are  of 
definite  sizes,  the  food  we  eat  has  a  certain  weight,  and  you 
go  to  class  for  a  definite  length  of  time.     All  these  quantities 
are  definite,  and  in  order  to  express  them  we  must  have 
definite  units. 

This  is  not  a  new  thing,  for  we  have  been  using  units  all 
through  this  course,  but  it  is  advisable  to  study  them  for 
their  own  sake. 

268.  The  English  System.  —  There  are  two  great  sys- 
tems of  measurement  —  the  English  and  the  Metric.     There 
is  no  necessity  for  two  systems,  but  we  have  them,  and 
people  will  continue  to  use  both  for  many  years  to  come. 

There  are  other  things  to  be  measured,  but  the  three 
principal  ones  are  space,  mass  (incorrectly  called  weight),  and 
time. 

Under  space,  come  length,  area,  and  volume.  The  English 
unit  of  length  is  the  foot.  Other  units  are  derived  from 
this  ;  the  yard  =  3  ft. ;  the  inch  =  yV  ft. ;  the  mile  =  5280  ft. 

The  unit  foot  is  made  definite  by  the  fact  that  the  original 
is  kept  in  London.  Copies  of  it  are  made  and  used  as 
standards  of  measurement.  Our  standard  is  kept  at 
Washington. 

227 


228 


MECHANICS   OF   SOLIDS 


FIGURE  241. — A 
CUBIC  FOOT. 


The  units  of  area  and  volume  are  derived  from  the  units 
of  length.     Thus  the  square  foot  is  an  area  which  is  one  foot 
on  a  side ;  the  cubic  foot  is  a  cube  which 
is  one  foot  on  each  edge.     (Figure  241.) 

Other  units,  such  as  square  yard,  cubic 
yard,  square  inch,  cubic  inch,  etc.,  have 
similar  meanings. 

The  unit  of  mass  is  the  pound  (lb.), 
and  it  denotes  a  certain  amount  of 
matter  determined  by  a  standard  kept 
in  the  same  way  as  the  standard  foot.  Other  units  are 
derived  from  it,  such  as  the  ounce  (oz.)  =  -j^  lb. ;  the  ton 
(T.)  =  2000  lb. ;  etc. 

The  unit  of  time  is 
the  second  (sec.) ;  it  is 
based  on  the  time  it 
takes  the  earth  to 

make  one  rotation  on  its  axis.  The  second  is  ^eJoT  °f  that 
time.  The  other  units  derived  from  it  are  the  minute 
(min.)  =  60  sec. ;  the  hour  (hr.)  =  60  min. ;  the  day  =  24 
hr. ;  the  year  =  365 \  days. 


FIGURE  242.  —  THE  STANDARD  METER. 


FIGURE  243.  —  UNITED  STATES  NATIONAL  PROTOTYPE  METER  BAR, 
Bureau  of  Standards,  Washington,  D.  C. 


THE   TWO  SYSTEMS  COMPARED  229 

269.  The  Metric  System.  —  The  same  quantities  can  be 
measured  in  the  metric  system,  but  the  units  are  different. 
The  unit  of  length  is  the  meter  (m.) ;  and  it  is  defined  as  the 
distance  between  two  scratches  made  on  a  platinum  bar 
kept  at  Paris.     (Figure  242.) 

Table  of  Lengths 

10  millimeters  (mm.)  =  1  centimeter  (cm.) 
100  cm.  =  1  meter  (m.) 

1000  m.  =1  kilometer  (km.) 

The  metric  unit  of  mass  is  the  gram  (gm.),  and  it  is  YoVo 
part  of  a  piece  of  brass  kept  in  Paris  along  with  the  standard 
meter.  This  piece  of  brass  was  so  made  that  it  has  the 
same  mass  as  1000  c.c.  of  pure  water  at  4°  C.  That  makes 
the  gram  equal  to  the  mass  of  1  c.c.  of  pure  water  at  4°  C. 

Other  units  are  given  in  the  table. 

Table  of  Masses 

1000  milligrams  (mg.)  =  1  gram  (gm.) 
1000  gm.  =  1  kilogram  (kg.) 

The  metric  unit  of  time  is  the  second.  It  is  identical  with 
that  of  the  English  unit. 

270.  The  Two  Systems  Compared.  —  Just  a  glance  at 
the  two  systems  is  sufficient  to  show  that  the  metric  is  much 
the  simpler. 

All  the  derived  units  in  the  metric  system  are  multiples 
of  ten.  For  example,  10  mm.  =  1  cm.,  100  cm.  =  1  m., 
1000  m.  =  1  km.,  etc.  This  makes  it  easy  to  remember  and, 
at  the  same  time,  easy  to  change  from  one  unit  to  another. 
All  that  is  necessary  is  to  move  the  decimal  point  either  to 
the  right  or  left.  For  example : 


230  MECHANICS   OF   SOLIDS 

1.273  m.    =  127.3  cm. 
467.8  cm.  =  4.678  m. 
3.642  kg.   =  3642  gm. 

In  the  English  system  this  is  not  true.  There  is  no 
regularity  whatever.  This  makes  it  hard  to  change  from 
one  unit  to  another.  For  example  : 

15  ft.  =  15  X  12  =  180  in. 
231  in.  =  ^  =  19J  ft. 

3  Ib.  =  3  X  16     =48  oz. 
90  oz.  =  f  jf  =  5|  Ib. 

271.  Relation  between  the  Two   Systems.  —  So  long  as 
there  are  two  systems  in  use,  we  shall  at  times  be  obliged 
to  change  readings  in  one  to  readings  in  the  other.     For  this 
reason  we  need  a  table  of  equivalents.     The  fact  that  the 
two  systems  are  entirely  independent  makes  these  equiva- 
lents irregular  and  burdensome. 

Table  of  Equivalents 
ENGLISH  METRIC 

in 2.54  cm. 

Ib.        . 453.6  gm. 

sec. 1  sec. 

sq.  in.       .     .     .     »     .     .     ,         6.452  sq.  cm. 

cu.  in.      .     .     .     ....       16.39  c.c. 

liquid  qt -       .945  liter  (liquid  unit) 

Using  this  table  we  can  change  from  any  reading  in  one 
system  to  the  corresponding  readings  in  the  other  system. 

272.  Force.  —  Besides   space,  mass,  and   time   there   are 
many  other  physical  quantities  which  have  to  be  measured. 
One  of  these  is  force. 

Force  is  a  push,  or  a  pull,  on  an  object,  that  tends  to  make 
the  object  move.  The  force  may,  or  may  not,  make  the  object 
move,  but  it  always  tends  to  do  so.  For  example,  you  can 


UNITS  OF    WORK  231 

pull  on  a  chair  and  make  it  slide  on  the  floor.  Again,  you 
can  pull  or  push  on  the  corner  of  a  house,  and  it  will  not 
move,  but  there  is  a  tendency  to  move,  and  if  the  push  or 
pull  were  large  enough,  it  would  move.  These  are  examples 
of  force. 

273.  Units  of  Force.  —  Force  is  measured  in  both  the 
English  and  metric  systems. 

The  unit  most  used  in  the  English  system  is  the  pound. 
You  will  notice  that  this  is  the  same  name  as  that  given  to 
the  unit  of  mass,  but  the  idea  is  different. 

A  pound  mass  is  a  certain  amount  of  matter.  A  pound 
force  is  the  pull  of  the  earth  on  a  pound  mass  at  sea  level. 

The  unit  most  used  in  the  metric  system  is  the  gram. 
Again,  this  is  the  same  name  as  that  given  to  the  unit  of 
mass,  and,  as  in  the  English  system,  it  represents  the  pull  of 
the  earth  on  a  gram  mass  at  sea  level. 

274.  Work.  —  When  a  force  produces  motion,  it  is  said 
to  do  work.     Work  is  a  definite  physical  quantity  and  can 
be  measured.     When  you  pull  on  a  chair,  and  it  slides  on  the 
floor,  you  do  work;   but  if  you  do  not  pull  hard  enough  to 
make  it  slide  or  move,  there  is  no  work  done. 

Work  is  the  result  of  a  force  acting  against  a  resistance  and 
moving  it.  The  amount  of  work  is  measured  by  the  force 
multiplied  by  the  distance  the  force  moves. 

Work  =  Force  X  Distance. 

It  will  be  seen  that  if  the  object  is  not  moved,  no  work 
will  be  done ;  or,  if  the  body  be  moving  without  any  force 
applied,  no  work  is  done. 

275.  Units  of  Work.  —  The  unit  of  work  in  the  English 
system  is. the  foot-pound,  and  in  the  metric  system  it  is  the 
gram -centimeter. 


232  MECHANICS   OF   SOLIDS 

A  foot-pound  is  the  work  done  when  a  pound  force  acts 
through  a  distance  of  one  foot. 

If  you  were  to  pull  a  chair  on  the  floor  a  distance  of  3 
ft.  and  it  took  a  force  of  5  lb.,  the  work  done  would  be 

3  X  5  =  15  ft.  lb. 

To  find  the  work  done,  multiply  the  force  by  the  distance 
it  moves. 


CHAPTER  XXII 


MACHINES 

276.  Machines.  —  A  machine  is  a  mechanical  apparatus 
which  either  transforms  or  transfers  energy.     There  are  six 
simple  machines.     They  are  lever,  wheel  and  axle,  inclined 
plane,  pulley,  screw,  and  wedge. 

All  other  machines  are  composed  of  a  combination  of  one 
or  more  of  these  six.  For  example,  a  sewing  machine  has  a 
combination  of  the  lever,  pulley,  and  screw.  Even  the  most 
complicated  machine,  such  as  the  modern  printing-press,  is 
made  of  groups  of  the  six  simple  machines. 

277.  The  Lever.  —  The  lever  consists  of  a  rigid  bar  (B) 
Figure  244,  a  weight  (W),  a  force  (F),  and  a  pivot  (P).     W 
represents    the  force 

overcome,  which  is 
often  the  weight  of 
an  object  being  lifted ; 
F  represents  the  force 
applied;  while  P  is  the 
point  about  which  the 
bar  turns. 

The  distance  (a)  from  the  force  to  the  pivot  is  called 
the  force-arm.  The  distance  (b)  from  the  weight  to  the  pivot 
is  called  the  weight-arm.  The  product  of  the  force  and 
the  force-arm  is  the  force  moment  (F  a),  and  the  product  of 
the  weight  and  weight-arm  is  the  weight  moment  (W  b). 

233 


FIGURE  244. — THE  LEVER; 


234 


MACHINES 


The  law  of  the  lever  is  that  the  force  moment  equals  the 
weight  moment,  or  F  a  =  W  b. 

278.  Classes  of  Levers.  —  Levers  are  divided  into  three 
classes,  according  to  the  relative  positions  of  the  force,  the 

weight,  and  the  pivot. 
The  first  class  has 
the  weight  and   the 
force  on  the  ends  and 
the     pivot     in     the 
middle.   (Figure  245.) 
The    second    class 
has    the    force    and 


on 


the 


FIGURE  246.  —  SECOND  CLASS  LEVER. 


FIGURE  245.  —  FIRST  CLASS  LEVER. 

the     pivot 
ends  and  the  weight  in  the  middle.     (Figure  246.) 

The  third  class  has  the  weight  and  the  pivot  on  the  ends 
and  the  force  in  the 
middle.  (Figure  247.) 
279.  Mechanical 
Advantage.  —  In  dis- 
cussing a  machine, 
the  term  mechanical 
advantage  is  used. 
Every  machine  has  a  mechanical  advantage,  and  this  is 
found  by  dividing  the  weight  by  the  force,  or  by  finding  an 

equal  ratio.  Thus  it 
has  a  definite  mean- 
ing, and  is  defined  as 

W 

the  fraction  —  • 
r 

In  the  case  of  the 
Therefore    to    find    the 


FIGURE  247. —THIRD  CLASS  LEVER. 


lever  - 

b 


W 
F 


~;        (Figure    244.) 


APPLICATIONS  OF   THE  LEVER 


235 


mechanical  advantage  of  a  lever,  divide  the  force-arm  by 
the  weight-arm,  or 

I  IT    L      •    /    j      4  Force-arm 

Mechanical  advantage  =  rrr  .          — 
Weight-arm 

280.   Efficiency.  —  Another  term    used    in  discussing    a 
machine  is  efficiency.     This  term  also  has  a  definite  meaning, 

j  •    j  .c      i       ,v     j      ,•       work-out 

and  is  denned  as  the  traction — —  - 

work-in 

No  machine  will  do  work  of  its  own  accord.  Work  must 
first  be  put  into  it,  and  then  it  will  do  work,  giving  a  cer- 
tain amount  out.  The 
work-in  is  the  work  put 
into  the  machine.  The 
work-out  is  the  work 
that  the  machine  gives 
out  when  operated. 

A  machine  never  gives 
out  as  much  work  as  is 
put  into  it,  because  some 


FIGURE    248.  —  BALL    BEARINGS    REDUCE 
FRICTION  AND  INCREASE  THE  EFFICIENCY. 


of  the  work  is  always 

lost    in    the    machine, 

overcoming  friction.     Therefore  the  efficiency  of  a  machine 

is  always  less  than  100  per  cent. 

In  the  case  of  a  lever  there  is  usually  very  little  friction 
and  so  the  efficiency  is  usually  from  95  per  cent  to  99.9  per 
cent. 

281.  Applications  of  the  Lever.  —  There  are  many  appli- 
cations of  the  lever,  but  one  that  needs  especial  mention  is 
the  balance  used  for  weighing  objects.  (Figure  249.) 

The  balance  consists  of  a  beam  (B)  supported  on  a  knife- 
edge  (K).  At  each  end  of  the  beam  is  hung  a  scale  pan  (S). 
These  are  also  supported  on  knife-edges.  A  pointer  (P) 


236 


MACHINES 


is  attached  to  the  beam 
to  show  when  a  balance 
of  the  weights  is  ob- 
tained. 

To  make  a  weighing, 
the  object  to  be  weighed 
is  placed  in  the  left-hand 
pan  and  is  the  W  of  the 
lever.  Standard  weights 
are  placed  in  the  right- 
hand  pan,  so  that  a 
balance  is  obtained. 

The  best  method  to 
get  a  balance  is  to  start 
with  the  largest  weight. 
If  it  is  too  small,  add 
the  next  one,  and  so  on. 
If  it  is  too  large,  take  it 
off  and  use  the  next  smallest.  Repeat  this  operation  until 
a  balance  is  obtained,  that  is,  until  the  pointer  will  swing 
the  same  distance  on  one  side  as 
on  the  other. 

The  balance  is  a  lever  of  the  first 
class.  Other  examples  are  shown  in 
Figures  250,  251,  252. 

Figures  253,  254,  255  show  applica- 
tions of  the  second  class  lever. 

Figures  256,  257,  258  show  applica- 
tions of  the  third  class  lever. 

Make  a  simple  drawing  and 
classify  the  levers  in  the  following 
examples. 


FIGURE  249.  —  THE  WEIGHING  BALANCE 
is  A  LEVER. 


FIGURE  250.  — THE  CAN 
OPENER  USED  AS  A  FIRST 
CLASS  LEVER. 


APPLICATIONS  OF   THE  LEVER 


237 


FIGURE  251. — THE  TACK 
PULLER  USED  AS  A 
FIRST  CLASS  LEVER. 


FIGURE  253.  —  A  CAN 
OPENER  USED  AS  A 
SECOND  CLASS  LEVER. 


FIGURE  252.  —  SCISSORS  ILLUSTRATE 
A  FIRST  CLASS  LEVER. 


FIGURE    254.  —  A     POTATO     RICER 
USED  AS  A  SECOND  CLASS  LEVER. 


FIGURE  255.  —  A  NUT  CRACKER  is 
A  SECOND  CLASS  LEVER. 


FIGURE  256.  —  GRASS  CUTTERS  OR 
SHEEP  SHEARS  ILLUSTRATE  THIRD 
CLASS  LEVER. 


FIGURE  257.  — THE  SUGAR  TONGS 
is  A  THIRD  CLASS  LEVER. 


238 


MACHINES 


1.  Wire  pliers 

2.  Pitcher  pump 

3.  Lemon  squeezer 

4.  Spoon 

5.  Knife 

6.  Fork 

7.  Claw  hammer  pulling  a  nail 


8.  Oar  of  rowboat 

9.  Paddle  of  canoe 

10.  The  human  arm 

1 1 .  Wheelbarrow 

12.  See-saw 

13.  Spring-board 

14.  Shovel 


Name  five  other  applica- 
tions of  the  lever,  and 
classify  them. 

282.   Wheel  and  Axle.  - 
The  wheel   and  axle   is  an- 
other simple   machine   very 
similar  in  action  to  the  lever. 

It  consists  of  a  wheel  and 
an  axle  rigidly  fastened  to- 
gether. (Figure  259.)  The 
force  (F)  acts  on  a  rope 
wound  around  the  wheel, 


FIGURE  258. — -A  BROOM  USED  AS  A 
THIRD  CLASS  LEVER. 


FIGURE  259.  — THE 
WHEEL  AND  AXLE. 


INCLINED   PLANE 


239 


and  the  weight  (IV)  is  hung  on  a  rope  wound  in  the  opposite 
direction  on  the  axle. 

When  the  force  moves  down,  the  weight  moves  up.     The 
action  is  the  same  as  in  the  lever. 
The  radius  (R)  of  the  wheel  acts  as 

the  force-arm,  and  the  radius  (r)  of        /  •&//  \\F 

the  axle  acts  as  the  weight-arm. 

The  mechanical  advantage  of  the 

wheel   and    axle  is  —  or,  as  in  the 
r 

R 

lever,  —  • 
r 

The  efficiency  of  this  machine  is 

less  than  that  of  the  lever,  ranging   FIGURE  260.     ANOTHER 
„  FORM  OF  THE  WHEEL  AND 

from    60   per  cent  to  99  per  cent.      AxLE 
The    efficiency    depends    upon    the 

bearings  of  the  machine  and  upon  the  flexibility  of  the  cord. 
Sometimes  a  crank  is  used  instead  of  the  wheel.      (Figure 
260.)     This  does  not  change  the  action. 

283.  Applications  of  Wheel  and  Axle.  —  The  windlass 
used  in  removing  dirt  from  wells  or  manholes  in  the  street  is 
an  application  of  the  wheel  and  axle.  (Figure  261.) 

Another  application  of  the  wheel  and  axle  is  the  device 

used     for     raising     awnings. 
(Figure  262.) 

Name  and  draw  two  other 
applications  of  the  wheel  and 
axle. 

284.  Inclined  Plane.— The 
inclined  plane  consists  of  a 

FIGURE  261. -THE  WINDLASS  Is  A    Plane   set  at . an    anSle   to    the 

WHEEL  AND  AXLE.  horizon.     (Figure  263.)     The 


240 


MACHINES 


weight  (W)  always  acts  downward,  and  the  force  (F)  acts 
along  the  plane.     The  vertical  distance   (h)   is  called  the 

height  of  the  plane,  while  the 
distance  along  the  plane  (L) 
is  called  the  length  of  the  plane. 
The  force  (F)  must  move 
the  length  of  the  plane  (L) 
in  order  to  raise  the  weight 
(W)  the  height  (h). 
The  mechanical  advantage 


of  the  inclined 


i         •      W 
plane  is  — - 

r 


or 


It  will  be  seen  from 


this  that  the  more  nearly  the 
FIGURE  262. -A  WHEEL  AND  AXLE       lane  comeg  to  the  horizontal, 
Is  OFTEN  USED  TO  LIFT  AWNINGS.       ,  ... 

the  greater  will  be  the  me- 
chanical advantage.  Then,  in  order  to  lift  a  large  weight, 
use  a  long  plane. 

285.  Applications  of  Inclined  Plane.  —  There  are  many 
applications  of  the  inclined  plane.  Figure  264  shows  an  in- 
clined plane  used  for  loading  a  piano  into  a  truck.  A  heavy 
plank  is  used  for  the  plane  and  the  height  of  the  truck  is  the 
height  of  the  plane. 
By  this  means  one  or 
two  men  can  push 
the  piano  into  the 
truck. 

Another      applica- 
tion of  the  inclined  plane  is  the  rolling  stairway.     (Figure 
265.)     This  is  often  used  in  large  department  stores  instead 
of  elevators.     A  person  wishing  to  go  from  one  floor  to 


FIGURE  263. — THE  INCLINED  PLANE. 


PULLEY 


241 


another  steps  on  the  moving 
stairway  and  is  carried  up,  or 
down,  according  to  the  direction 
in  which  the  stairway  moves. 
Usually  there  are  two  of  .these  side 
by  side,  one  going  up,  and  the 
other  down. 

Graded    roads   are    excellent    ex- 
amples of  inclined  planes. 


FIGURE  264.  —  AN  INCLINED 
PLANE  USED  TO  LOAD  A 
PIANO  INTO  A  TRUCK. 


(Figure 


286.   Pulley.  —  There  are  two  types  of  pulleys. 
266  and  Figure  267.) 

Figure    266    shows   two   pulleys    belted   together.      The 
one   which   supplies   the    power    is    called    the    driver,   and 

the  other  the   driven. 


FIGURE  265.  —  A  MOVING  STAIRWAY  Is  AN 
INCLINED  PLANE. 

The  larger  the  driven  pulley  is, 
the  greater  the  mechanical  ad- 
vantage. 


FIGURE  266. — Two  PULLEYS  BELTED 
TOGETHER. 


a 

w 

FIGURE  267.  —  AN- 
OTHER TYPE  OF 
PULLEY. 


242 


MACHINES 


Tne  mechanical  advantage  = 


radius  of  driven       R 


radius  of  driver        r 
Figure  267  shows  the  other  type  of  pulley,  often  called  a 
block.     A  block  consists  of  one  or  more  pulleys  or  sheaves 

fastened  side  by  side,  or 
one  above  the  other,  so 
that  they  are  free  to  turn. 
Two  blocks  are  used 
to  lift  a  weight.  One 
block  is  made  fast,  and 
the  weight  is  attached 
to  the  other  one.  A 
rope  or  chain  is  threaded 
through  the  blocks,  as 
shown  in  the  figure. 

The  mechanical  ad- 
vantage is  equal  to  the 
number  of  strands  sup- 
porting the  weight. 

From  the  figure  it  will 
be  seen  that  if  the  weight 
be  lifted  1  foot,  there  are 
six  strands  to  be  short- 
ened 1  foot.  This  allows 
the  force  (F)  to  move  6 
feet  while  the  weight 
moves  1  foot.  Thus  the 
mechanical  advantage  is 
six. 

287.  Applications  of  the  Pulley.  —  A  familiar  example  of 
the  first  type  of  pulley  is  the  sewing  machine.  (Figure  269.) 
Here  the  large  wheel  is  the  driver,  and  the  small  wheel  is  the 


FIGURE  268.  —  A  LABORATORY  SET  OF 
PULLEYS. 


APPLICATIONS  OF   THE  PULLEY 


243 


driven.     This  arrangement  makes  it  harder  to  turn,  but  a 
greater  speed  can  be  obtained. 

The  revolutions  per  minute  (R.  P.  M.)  of  two  pulleys  belted 
together  are  inversely  as  their  diameters.  This  means  that  the 
large  pulley  runs  slowly  while  the  small 
one  runs  fast. 

Problem:  If  a  driver  is  2  ft.  in  diameter, 
and  makes  500  R.  P.  M.,  what  is  the  speed  of 
the  driven,  which  is  f  ft.  in  diameter  ? 


The   second   type   of  pulley  is  often    I 
used    in   lifting    safes    or    other   heavy    FIGURE   269.  — THE 

i    .  /-rr  ^i-rn  \  A  1  PULLEY    AS    USED     IN 

Objects.       (Figure  270.)      A    gin   pole   IS         THE  SEWING  MACH.NE. 

placed  in  the  window  above,  and  the 

upper  block  is  fastened  to  this.     By  pulling  on  the  free  end 

of  the  rope  the  safe  is  raised  to  the  open  window.     From 

here  it  is  swung  inside. 

Elevators  are  usually  lifted  up 

and   let  down  by  means  of  this 

type  of  pulley. 


FIGURE  270.  — A  SET  OF  PUL- 
LEYS USED  TO  LIFT  HEAVY 
OBJECTS  TO  THE  UPPER 
STORIES  OF  HIGH  BUILDINGS. 


FIGURE  271.  —  A  JACK  SCREW. 


244 


MACHINES 


FIGURE  272. —  A  WEDGE. 


288.  Screw  and  Wedge.  —  The  screw  and  the  wedge  are 
both  very  much  the  same  as  the  inclined  plane.     As  is  shown 
by  Figure  271 ,  the  screw  is  merely  a  spiral  inclined  plane  which 

is  made  to  move 
under  the  weight, 
thus  forcing  the 
weight  to  move. 

Likewise  Figure 
272  shows  that  the 
wedge  is  a  double 
inclined  plane,  made 
to  move  under  the 
weight,  causing  the 
latter  to  move. 

The  pitch  of  a  screw  is  the  number  of  threads  per  inch,  and 
the  distance  from  one  thread  to  the  next  is  called  the  lead 
(L).  The  mechanical  advantage  is  the  circumference  of  the 
circle  that  the  force  moves  divided  by  the  lead,  or 

Mechanical  advantage  = 

±j 

The  mechanical  advantage  of  the  wedge  is  the  length  of  the 
wedge  (L)  divided  by  the  thickness  of  the  wedge  (h),  or 

Mechanical  advantage  =  — 

h 

The  efficiency  of  the  screw  and  the  wedge  is  small,  because 
there  is  always  much  friction. 

289.  Application  of  the  Screw  and  Wedge.  —  The  use  of 
the  screw  is  common,  and  many  illustrations  could  be  named. 
A  few  are  the  piano  stool  (Figure  273),  the  ordinary  wood 
screw  (Figure  274),  and  the  bolt  and  nut  (Figure  275). 

The  wedge  is  not  in  such  common  use,  but  many  examples 


POWER 


245 


can  be  found.  Figure  276 
shows  a  hatchet  used  as  a 
wedge  to  split  kindling. 

290.  Power.  —  Power  is 
the  time  rate  of  doing  work. 
It  is  very  often  confused 
with  the  term  work;  but  it 
is  different,  for  it  involves 
the  idea  of  time,  while  work 
does  not. 

A  boy  could  carry  a  thou- 
sand bricks  up  a  ladder  10  ft. 
high  as  well  as  a  man,  but  it 
would  take  him  longer. 

The  amount  of  work  done 
by  the  boy  and  man  would 

be  the  same,  but  the  rate  at  which  the  man  would  do  the 
work  would  be  greater ;   so  we  say  he  has  the  more  power. 

The  units  of  power  are  the  foot-pound  per  second,  and  the 
gram-centimeter  per  second.  These  units  are  so  small  that 
larger  units  are  commonly  used.  The  horsepower  is  the  one 
most  common  in  this  country.  A  horsepower  is  the  power 
that  will  do  33000  foot-pounds  of  work  per  minute. 

To  find  the  horsepower  delivered  in  any  case,  find  the 
work  in  foot-pounds  done  per  minute, 
and  divide  by  33000 ;  thus  : 


FIGURE  273.  —  THE  PIANO   STOOL  Is 
AN  APPLICATION  OF  THE  SCREW. 


FIGURE  274.  —  THE 
WOOD  SCREW. 


FIGURE  275. —THE  BOLT  AND  NUT  Is 
AN  APPLICATION  OF  THE  SCREW. 


246 


MACHINES 


If  a  girl  weighs  120  pounds  and  climbs  the  stairs  from  one  floor  to  the 
next,  a  distance  of  15  ft.,  in  30  seconds,  she  does  120  X  15  =  1800  ft.- 
Ib.  in  .5  min.  (30  sec.)  or 


1800 
.5 


3600  ft.-lb.  per  min. 


33000 


6. 
55 


ho        ower 


291.  Power  Delivered  by  Pulleys.  —  It  is  often  desirable 
to  know  the  power  necessary  to  run  certain  appliances  in  the 

home,  such,  for  example, 
as  the  sewing-machine, 
the  vacuum  cleaner,  the 
washing-machine,  food 
chopper,  bread  mixer, 
etc.  Most  of  these  are 
either  run  by  pulleys 
driven  by  belts  or  by 

gears,  SO  the  method  for 
findm  ^  horsepower  is 
the  same. 

Let  us  compute  the  horsepower  for  a  sewing  machine  as  an 
example. 

Suppose  the  small  3-in.  wheel  of  the  sewing  machine  must  make 
500  R.  P.  M.,  and  that  the  belt  has  an  effective  pull  of  2  Ib.  What  is 
the  horsepower  necessary  to  run  it  ? 

Method  : 

3  inches  =  —  =  .25  ft. 

.25  X  3.1416  =  .7854  ft.,  cir.  of  wheel 
.7854  X  500  =  392.7  ft.,  distance  the  belt  moves  in  1  min. 
392.7  X  2  =  785.4  ft.-lb.  per  min. 

785.4 


FIGURE  276.  —  THE  HATCHET  USED  IN 
SPLITTING  KINDLING  Is  AN  APPLICATION 
OF  THE  WEDGE. 


33000 


.0238,  horsepower  required. 


PROBLEMS  247 

What  horsepower  is  necessary  to  run  a  food  chopper  that  requires  a 
force  of  10  Ib.  on  the  end  of  a  1-ft.  crank  making  60  R.  P.  M.  ? 
Method  : 

2  ft.  =  diameter  of  circle 
2  X  3.1416  =  6.2832  ft.,  cir.  of  circle 
6.2832  X  60  =  376.992  ft.,  distance  force  moves  in  1  min. 
376.992  X  10  =  3769.92  ft.-lb.  per  min. 
3769.92 


33000 


.114,  horsepower  required. 


Problems 


1.  The  pulley  on  a  washing-machine  is  10"  in  diameter  and  makes 
100  R.  P.  M.     The  belt  has  an  effective  pull  of  25  Ib.     What  horse- 
power is  required  ? 

2.  The  pulley  on  a  kitchen  power-table  is  6"  in  diameter  and  makes 
600  R.  P.  M. ;  the  effective  pull  on  the  belt  is  10  Ib.     What  horsepower 
is  required  ? 

3.  If  a  motor  of  80  per  cent  efficiency  runs  the  pulley  in  Prob.  1, 
how  many  watts  does  it  require?  (746  watts  =  1  horsepower.) 

4.  If  a  motor  of  85  per  cent  efficiency  runs  the  pulley  in  Prob.  2, 
how  many  watts  does  it  require  ? 

5.  When  you  turn  an  ice-cream  freezer  handle  1  ft.  long,  50  R.  P.  M., 
and  it  requires  a  force  of  8  Ib.,  what  horsepower  are  you  producing? 


CHAPTER   XXIII 
DYNAMICS 

292.  Motion.  —  Motion  is  a  change  of  position  with  refer- 
ence to  some  other  object. 

If  you  were  to  look  at  a  book  lying  near  the  center  of  a 
table  and  were  then  to  close  your  eyes,  and  if,  while  they 
were  closed,  some  one  were  to  change  the  book  to  the  edge 
of  the  table,  could  you  tell  that  it  had  been  moved,  when 
you  opened  your  eyes  ?  You  say  "  Yes  "  ;  for  it  has  changed 
its  position  with  reference  to  the  table. 

Now,  if  you  were  to  try  the  experiment  again,  and  the 
person  changed  the  table  and  let  the  book  remain  in  the 
center  of  the  table,  could  you  tell  whether  the  book  had  been 
moved?  Some  would  say  "  Yes,"  and  some  "No."  Both 
are  right  and  both  are  wrong,  depending  on  what  is  taken  as 
a  point  of  reference.  Explain. 

293.  Newton's  Three  Laws  of  Motion.  —  It  always  takes 
force  to  produce,  or  to  change,  motion.     A  chair  cannot  be 
moved  unless  some  force  is  applied.     Also,  anything  in  mo- 
tion requires  a  force  to  stop  it  or  make  it  change  its  direction. 

Newton  learned  this  fact  and  put  it  into  three  laws : 

1.  Every  body  continues  in  a  state  of  rest,  or  of  uniform 
motion  in  a  straight  line,  unless  acted  upon  by  some  external 
force. 

2.  Every  motion  is  proportional  to  the  acting  force,  and 
takes  place  in  the  direction  in  which  the  force  acts. 

248 


APPLICATION  OF  NEWTON'S  LAWS  249 

3.  To  every  force  there  is  an  equal  force  in  the  opposite  direc- 
tion. 

294.  Meaning  and  Application  of  Newton's  Laws.  —  The 
first  law  means  that  if  a  body  is  at  rest,  it  has  a  tendency  to 
remain  at  rest.  This  is  shown  when  you  undertake  to  move 
a  table  or  some  other  heavy  object,  even  though  it  be  on  cas- 
ters. On  the  other  hand,  a  body  in  motion  tends  to  keep  on 
going  in  a  straight  line.  This  is  illustrated  by  the  skidding 
of  an  automobile,  either  around  corners  or  when  the  brakes 
are  set  quickly. 

The  tendency  which  a  body  has  to  remain  at  rest,  when  at 
rest,  or  to  continue  in  motion,  when  in  motion,  is  called 
inertia.  It  is  the  inertia  of  your  body  which  throws  you 
over  in  a  street  car  when  it  turns  a  corner,  or  which  jerks 
you  backward  or  forward  when  the  car  starts  or  stops 
suddenly. 

The  second  law  means  that  the  resulting  motion  is  doubled 
if  the  force  is  doubled,  or  multiplied  by  3  if  the  force  is  multi- 
plied by  3,  etc.  It  also  means  that  the  object  tends  to  move 
in  the  direction  in  which  the  force  acts. 

To  illustrate :  If  you  throw  a  ball  with  a  certain  force, 
it  will  have  a  certain  quantity  of  motion  ;  but,  if  it  is  thrown 
with  twice  the  force,  it  will  go  twice  as  fast ;  also  it  will  go  in 
the  direction  in  which  it  is  thrown,  if  no  other  force  acts 
upon  it. 

The  third  law  means  that  there  is  always  a  force,  called  the 
reaction,  which  acts  in  the  opposite  direction  to  any  given 
force. 

To  illustrate  this,  consider  your  own  weight.  This  force  is 
downward,  but  the  floor  pushes  upward  with  the  same  force ; 
otherwise  you  would  go  through  the  floor.  You  cannot  take 
hold  of  your  shoe-tops  and  lift  yourself,  for  every  pound  that 


250 


DYNAMICS 


FIGURE  277.— A  CLOTHES-LINE  POST 
WITH  BALANCED  FORCES. 


you  lift  is  counteracted  by  a  pound  in  excess  of  your  weight 
which  is  pushed  downward  by  your  feet. 

295.  The  Parallelogram  of 
Forces.  —  When  two  forces  act 
-J?  upon  a  body,  the  body  cannot 
move  in  both  directions,  but 
moves  in  the  direction  of  the 
resultant  of  those  two  forces. 
For  example,  a  clothes-line 
post,  as  in  Figure  277,  cannot 
move  in  both  the  directions 
AB  and  AC,  but  tends  to  move  along  the  resultant  AR, 
which  is  somewhere  between  AB  and  AC. 

To  find  the  resultant  of  two  forces  such  as  those  men- 
tioned above  we  use  what  is  called  the  parallelogram  of  forces. 
First,  lay  off  to  scale  lines  representing  the  forces  in  both 
amount     and     direction. 
(Figure  279.) 

For  example,  if  the  force 
AB  were  50  pounds,  and  the 
force  AC  were  30  pounds,  let 
5  inches  represent  the  50 
pounds  and  3  inches  repre- 
sent the  30  pounds.  Upon 
these  two  sides  construct  a 
parallelogram.  The  diagonal, 
which  is  5.83  inches,  repre- 
sents the  resultant  of  5.83  X 
10  =  58.3  pounds. 

In  this  way  the  result- 
ant of  any  two  forces 
may  be  found.  If  the 
original  forces  are  laid 


FIGURE  278.  —  A  LABORATORY  EXPERIMENT 
SHOWING  BALANCED  FORCES. 


APPLICATIONS  OF  PARALLELOGRAM  OF  FORCES     251 


off  to  a  certain  scale,  then  the  length  of  every  line  in  the 
figure  represents  the  amount  of  force  in  that  line. 

296.  Applications  of  Parallelogram  of  Forces.  —  The 
parallelogram  of  forces  can  be  used  to  determine  the  tension 
in  the  wires  in  picture-hanging. 


R 


20 


A  50*=  5"  B 

Scale   1*=10* 

FIGURE  279.  —  THE  PARALLELOGRAM 
OF  FORCES. 


FIGURE  280,  —  THE 
PARALLELOGRAM  OF 
FORCES  APPLIED  TO 
PICTURE  HANGING. 


Figure  280  shows  a  picture  hanging  from  a  hook  in  one  of  the  usual 
ways.  The  distance  between  the  supporting  screws  in  the  picture  is 
20  in.  The  distance  from  the  hook  to  the  line  of  screws  is  25  in.  Find 
the  tension  in  each  wire,  if  the  picture  weighs  10  pounds. 

Method: 

If  the  picture  were  supported  from  two  hooks  (A  and  B},  the  wires 
would  each  be  25  in.  long  and  would  support  -1?0-  =  5  pounds. 

Since  each  line  in  the  figure  represents  the  amount  of  force  in  that 
line,  then 

25  in.  =  5  Ib. 
1  in.  =  &  of  5=  ilb. 


The  actual  wire  CD  =  ^1  (AC)2  +  (AD)2  = 


-252 
/.  the  tension  in  CD 


-625  = 
26.9  Xi  =  5.38 Ib. 


=  26.9+ 


Problems 

1.  Find  the  tension  in  the  wire  of  a  picture  hung  from  a  hook  which 
is  12  in.  above  the  line  of  the  screws  in  the  picture,  if  the  two  screws 
are  18  in.  apart  and  the  picture  weighs  8  Ib. 


252  DYNAMICS 

2.  What  is  the  tension  in  a  guy-wire  for  a  clothes-line  post,  if  the 
post  is  6  ft.  high  and  the  guy- wire  is  set  4  ft.  from  the  base  of  the  post, 
the  clothes-line  having  a  tension  of  75  Ib.  ? 

297.  Velocity  and  Acceleration.  —  Any  body  in  motion 
has  a  definite  speed  or  velocity  —  two  terms  meaning  the  same 
thing. 

Velocity  is  the  time  rate  of  motion.  This  means  that  the 
number  of  units  of  distance  passed  over  per  unit  of  time  is 
velocity. 

To  say  that  the  velocity  of  a  train  is  30  miles  per  hour 

(sometimes  written  30  — '-  }  means  it  would  travel  30  miles 
hr.  J 

in  one  hour,  if  it  ran  at  that  rate  of  speed.     Other  units  of 
velocity  are 

ft.      cm.     km. 

J— ,   •  -,   — ,  etc. 

sec.     sec.      hr. 

If  the  speed  of  an  object  is  the  same  continuously,  it  is 
said  to  have  uniform  velocity.  But  if  the  velocity  changes 
it  is  said  to  be  accelerated. 

Acceleration  is  the  change  in  velocity  per  unit  time.  For 
example,  if  a  body  starts  from  rest  and  is  going  at  the  rate 

of  5  — -  at  the  end  of  the  first  second  ;    10  J!^-Lat  the  end  of 
sec.  sec. 

the  second  second ;  15  —  at  the  end  of  the  third  second, 
sec. 

etc.,  the  motion  is  said  to  have  an  acceleration  of  5  ft.  per  sec- 
ond, per  second,  meaning  that  it  has  gained  5  -1— ^  of  velocity 

sec. 

every  second. 

Acceleration  is  either  positive  or  negative,  according  as  the 
change  in  velocity  is  an  increase  or  a  decrease. 


UNIFORMLY  ACCELERATED   MOTION  253 

The  pull  of  gravity  gives  all  bodies  an  acceleration  down- 
ward of  32.2  ft.  per  second,  per  second,  or  980  cm.  per  second, 
per  second.  This  is  called  the  acceleration  due  to  gravity, 
and  is  represented  by  the  letter  g. 

298.  Uniformly  Accelerated  Motion.  —  When  a  body  is 
uniformly  accelerated,  it  is  very  often  desirable  to  find : 

(1)  The  velocity  (v)  in  terms  of  the  acceleration  (a)  and 
the  time  (t)  which  the  body  has  traveled  — 

v  =  at] 

(2)  The  distance  (S)  which  the  body  has  traveled  in  terms 
of  the  acceleration  (a)  and  the  time  (t)  which  the  body  has 

traveled  — 

S  =  i  at2 ; 

(3)  The  distance  (d)  which  the  body  has  traveled   in  any 
particular  second  in  terms  of  the  acceleration  (a)  and  the 
second  (t)  in  question  — 

d  =  J  a  (2  t  -  1) ; 

(4)  The  velocity  0)  in  terms  of  the  acceleration  (a)  and  the 
distance  passed  over  (S)  - 

vz  =  2  aS. 
The  following  problems  illustrate  the  use  of  these  formulae  : 

Problem  (1) :   What  is  the  velocity  of  an  automobile  at  the  end  of 
5  seconds,  if  it  has  an  acceleration  of  2  ft.  per  second,  per  second  ? 
Method  : 

v  =  at 

.-.  v  =  2.5  =  10^-      (ans.) 
sec. 

Problem  (2) :  How  far  will  a  train  travel  in  10  seconds,  if  it  has  an 
acceleration  of  \  ft.  per  second,  per  second  ? 

Method  : 

S  =  \  off- 
/.  S  =  *  .  J.     102  =  \  •  J  -  100  =  25  ft.     (ans.) 


254  DYNAMICS 

Problem  (3) :  How  far  will  a  train  travel  during  the  8th  sscond  after 
starting,  if  it  has  an  acceleration  of  ^  ft.  per  second,  per  second  ? 
Method: 

d  =  \  a  (2  t  -  1) 

/.  d  =  }.  }(2.  8-1)  =1-1(16-1) 
=  1-i.  15  =3f//.     (ans.) 

Problem  (4) :  What  is  the  velocity  of  an  automobile  after  it  has  gone 
25  ft.,  if  it  has  an  acceleration  of  2  ft.  per  second,  per  second? 
Method  : 

v*  =  2  aS 
/.  v*  =  2 .  2  •  25  =  100 

v  =  VlOO  =  10  -^-      (ans.) 

All  the  examples  above  were  given  in  the  English  system. 
The  same  formulae  and  methods  of  solution  are  used  in  the 
metric  system.  Instead  of  feet  use  centimeters. 

Since  the  pull  of  the  earth  gives  all  bodies  a  uniform  accel- 
eration, these  same  formulae  apply  to  freely  falling  bodies. 

For  falling  bodies  the  above  formulae  may  be  written  and 
used  in  the  special  forms : 

v  =  gt. 
S  =  \  cjt\ 
d  =  ±g(2t-  1). 
v*  =  2  gS. 

299.  Momentum.  —  The  quantity  of  motion  which  a  body 
possesses  is  called  momentum.  It  is  measured  by  multiplying 
the  mass  of  a  body  by  its  velocity.  Thus  an  automobile 

7777 

weighing  2500  Ib.  and  going  20  ~^  has  2500  X  20  =  50,000 

hr. 

Ib.-miles  per  hour  of  momentum. 

Likewise,  a  baseball  weighing  5  oz.  and  going  100  ft.  per 
sec.  has  a  momentum  of  ^  •  100  =  31 J  Ib.-ft.  per  sec. 

There  is  no  definite  unit  for  momentum,  so  terms  such  as 


FORCE   TO   OVERCOME  INERTIA  255 

lb.-mi.  per  hr.,  Ib.-ft.  per  sec.,  etc.,  have  to  be  used.  In  com- 
paring momenta,  care  must  be  taken  that  they  are  ex- 
pressed in  the  same  units. 

300.  Force  to  Overcome  Inertia.  —  By  Newton's  first  law 
of  motion  every  body  tends  to  remain  at  rest  or  to  continue  in 
a  straight  line  at  a  uniform  speed  unless  some  force  acts 
upon  it  ;  hence  a  force  setting  a  body  in  motion  (or  stopping 
its  motion)  must  overcome  this  inertia,  together  with  the 
other  forces  acting  upon  the  body,  such  as  friction,  weight, 
etc. 

The  force  to  overcome  inertia  is  proportional  to  both  the 
mass  of  the  body  and  the  acceleration  given  it.  Thus  : 

F  =  Ma  (1) 

F  =  ^-  (2) 

9 

If  the  mass  is  given  in  grams  and  the  acceleration  in  centi- 
meters per  second,  per  second,  equation  (1)  gives  the  force  in 
dynes.  If  the  weight  is  given  in  pounds  or  grams  and  the  accel- 
eration in  feet  per  second,  per  second,  or  centimeters  per  second, 
per  second,  equation  (2)  gives  the  force  in  pounds  or  grams  re- 
spectively. 

Thus  a  girl  weighing  1  10  Ib.  and  standing  in  an  elevator  going  down 
with  an  acceleration  of  2  ft.  per  second,  per  second,  will  apparently 
weigh  103.2  b. 

p=Wa 


32.2 


.'.  she  weighs  6.8  Ib.  less  than  110  =  103.2  Ib.,  her  apparent  weight. 

If  the  elevator  were  going  up  with  an  acceleration  of  2  ft.  per  sec- 
ond, per  second,  she  would  weigh  6.8  Ib.  more,  or  110  +  6.8  =  116.8  Ib., 
her  apparent  weight. 


256 


DYNAMICS 


The  force  required  to  overcome  the  inertia  of  any  body  can 
be  found  in  a  similar  manner. 

301.  Force  to  Overcome  Friction.  —  Excepting  the  mo- 
tions  of    the    heavenly   bodies,    all    motions   are   opposed 
by    a    certain    amount    of    friction,    so    that    the    force 
changing   the  motion  of   a   body  must  overcome  the  fric- 
tion besides  overcoming  inertia  and  other  forces,  such  as 
weight,  etc. 

In  calculating  the  force  necessary  to  produce  motion  of  a 
body,  each  part  must  be  calculated  separately  and  the  results 
added. 

302.  Centrifugal  Force.  —  Any  body  moving  in  the  cir- 
cumference of  a  circle  (Figure  281)  tends  to  fly  away  from 

the  center.     This  is  due  to  Newton's 
first  law  of  motion.     Explain. 

The  force  tending  to  throw  the  body 
away  from  the  center  is  called  the 
centrifugal  force. 

A  pail  of  water  may  be  swung  in  a 
vertical  plane  without  spilling  the 
water  on  account  of  the  centrifugal 
force.  Centrifugal  force  causes  ve- 
hicles to  skid  around  corners.  The 
cream  separator  uses  centrifugal  force  to  separate  the  cream 
from  the  milk.  This  can  be  done  because  cream  is  lighter 
than  plain  milk. 

303.  Energy   of  Motion.  —  All    bodies   in   motion   have 
energy    due    to    that    motion.      An    automobile    moving 
60  mi.  per  hour  will  do  more  damage,  if  it  smashes  into 
a  building,  than  if   it  were  running  10  mi.  per  hour.     A 
hammer  swung  with  the  arm  will  drive  a  nail  farther  than 
if  the  hammer  were  just  laid  on  the  nail.     These  are  all 


FIGURE  281.  —  CENTRIF- 
UGAL FORCE. 


GRAVITATION  257 

illustrations   of   energy  of   motion,   usually   called  Kinetic 
Energy  (KE). 

KE-™>. 


The  above  formula  will  give  the  kinetic  energy  in  foot- 
pounds if  W  is  expressed  in  pounds;  v  =  feet  per  second; 
and  g  =  32.2. 

304.  Gravitation.  —  Every  bit  of  matter  in  the  universe 
exerts  a  pull  on  every  other  bit  of  matter.  This  pull  is  called 
gravitation. 

The  earth,  being  a  very  large  bit  of  matter,  exerts  a  pull 
on  all  objects  on  or  near  it.  This  pull  is  called  the  weight 
of  the  object. 

Newton  formulated  three  laws,  called  Newton's  three  laws 
of  gravitation.  They  are  : 

1 .  The  weight  of  an  object  at  any  given  place  is  directly  pro- 
portional to  its  mass. 

2.  The  weight  of  an  object  above  the  surface  of  the  earth  is 
inversely  proportional  to  the  square  of  the  distance  from  the 
center  of  the  body  to  the 

center  of  the  earth. 

3.  The  weight  of  a  body 
below    the  surface  of  the 
earth   is  directly   propor- 
tional to  the  distance  be- 

FIGURE  282.  —  ILLUSTRATING  THE  SECOND 

tween  the  center  of  the  body  LAW  OF  GRAVITATION. 

and  the  center  of  the  earth. 

The  first  law  needs  no  explanation.  The  second  law  can 
be  made  more  clear  by  the  use  of  Figure  282. 

It  will  be  seen  that  the  farther  the  body  is  away  from  the 
earth,  the  fewer  are  the  lines  of  gravitation  which  pass 


258 


DYNAMICS 


through  it.     This  is  why  the  pull  gets  less  as  the  distance 
gets  greater. 

Figure  283  illustrates  the  third  law.     A  body  inside  the 
earth  has  part  of  the  earth  (A )  pulling  to  the  right,  while  the 

other  part  (B)  pulls  to  the 
left.  Thus  we  see  that  the 
resulting  force  becomes 
smaller  as  the  distance  be- 
tween the  center  of  the  body 
and  the  center  of  the  earth 
becomes  smaller. 

305.  Pendulum.  —  A  pen- 
dulum is  a  body  supported 
from  a  pivot  and  free  to 
swing  because  of  its  weight. 
(Figure  284.)  L  represents 
the  length  of  the  pendulum ; 

a,  the  amplitude  of  the  swing;   g,  the  acceleration  due  to 

gravity ;  t,  the  time  of  the  pendulum  —  the  time  it  takes  the 

pendulum  to  move  from  one  side  of  the  swing  to  the  other. 

There  are  four  laws  governing  the  time  of  a  pendulum : 

1.  The  time  is  independent 
of  the  mass. 

2.  The  time  is  independent 
of  the  amplitude. 

3.  The  time  is  directly  pro- 
portional to  the  square  root  of 
the  length. 

4.  The  time  is  inversely  proportional  to  the  square  root  cf 
the  acceleration  due  to  gravity. 

The  pendulum  is  used  to  regulate  clocks,  etc.     To  make 
a  clock  run  faster,  shorten  the  pendulum. 


FIGURE  283.  —  ILLUSTRATING  THE 
THIRD  LAW  OF  GRAVITATION. 


FIGURE  284.  —  THE  PENDULUM. 


CHAPTER   XXIV 
MECHANICS    OF   FLUIDS 

306.  The  Three  States  of  Matter.  —  All  matter  exists  in 
one  or  more  of  three  states  —  solid,  liquid,  or  gas.  Some 
substances  are  found  in  all  three  states.  Water  is  the  most 
common  of  these.  Other  substances  existing  in  the  three 
states  are  iron,  copper,  lead,  mercury,  etc. 

The  apparent  difference  between  the  three  states  of  matter 
is  as  follows : 

1.  A  solid  has  a  definite  shape  and  volume. 

2.  A  liquid  has  a  definite  volume,  but  takes  the  shape  of 
the  containing  vessel. 

3.  A  gas  has  neither  a  definite  shape  nor  volume,  but 
takes  the  shape  of  the  containing  vessel  and  fills  it  com- 
pletely. 

The  theoretical  difference  between  the  three  states  of 
matter  depends  upon  the  molecular  construction  of  the 
substance  in  these  different  states. 

In  a  solid,  the  molecules  are  close  together  and  are  held 
firmly  together  by  a  force  called  cohesion.  This  force  is 
sufficient  to  keep  the  molecules  from  changing  their  relative 
positions,  but  it  allows  them  to  vibrate. 

In  a  liquid,  the  molecules  are  farther  apart,  and  the  force 
of  cohesion  is  not  so  great.  The  molecules  can  slide  over 
one  another,  but  still  the  force  is  great  enough  to  keep  them 
from  separating. 

259 


260 


MECHANICS   OF   FLUIDS 


In  a  gas,  the  molecules  are  far  apart,  the  force  of  cohesion 
is  too  small  to  count,  and  the  molecules  fly  about  with  perfect 

freedom,  bumping  against  one 
another  and  the  sides  of  the  con- 
taining vessel. 

307.  Gases  and  Liquids  through 
Pipes.  —  The  fact  that  gases  and 
liquids  have  no  definite  shape 
makes  it  possible  to  deliver  them 
through  pipes. 

Consider  the  two  pipes  (a)  and 
(b)  (Figure  285)  filled  with  water 
coal,  respectively,   and   then   a   force  put 
In  the  first  case,  the  water  molecules 


FIGURE  285.  —  LIQUIDS  AND 
SOLIDS  IN  PIPES. 


and  chunks  of 
on  both  of  them, 
would  slide  over  one  another  at  the  bend 
of  the  pipe,  and  so  would  flow  around  the 
bend ;  but,  in  the  second  case,  the  chunks 
of  coal  would  not  slip  past  one  another, 
but  would  push  against  the  end  of  the 
pipe  and  would  clog  the  pipe.  A  gas 
would  act  in  the  same  way  as  the  water. 

Thus  we  see  why  it  is  possible  to  de- 
liver gas  and  water  through  pipes,  but 
why  we  have  to  haul  our  coal,  wood,  and 
all  other  solids. 

308.  Pressure.  —  Figure  287  shows  a 
cylinder  with  water  in  it,  and  a  piston 
(K)  being  forced  against  the  water  with 
a  force  of  100  Ib. 

It  will  be  seen  that  the  water  will 
push  on  the  end  of  the  cylinder  with  a 
force  of  100  Ib.  If  the  end  of  the  cylinder 


FIGURE  286.  —  PRES- 
SURE is  USED  IN 
THE  FIRE  EXTIN- 
GUISHER 


THE   HYDRAULIC   ELEVATOR 


261 


has  an  area  of  25  sq.  in.,  this  100  Ib.  will  be  distributed  over 
the  total  25  sq.   in.     Thus  each  square  inch  will  receive 

(P,  Figure  287.) 


—  =  4  Ib. 


The  force  on  the  one  square 
inch  is  called  the  pressure. 

Pressure  is  the  force  per  unit 
area.  It  is  found  by  dividing  the 
force  by  the  area  of  the  surface. 


FIGURE  287. —  MEANING  OF 
THE  TERM  "PRESSURE." 


Force  applies  to  the    total  area,  while  pressure   applies 
only  to  unit  area. 

309.  Pascal's  Law.  —  In  Figure  287  the  water  would 
press  not  only  on  the  end  of  the  cylinder,  but  also  on 
the  sides  ;  that  is,  every  square  inch  of  surface  would  also 

have  a  force  of  4  Ib.  ; 
or,  as  we  say,  the  pres- 
sure would  be  4  Ib.  per 
square  inch. 

Pascal  stated  these 
facts  in  the  form  of  a 
law  :  The  pressure  on  a 
confined  liquid  is  trans- 
mitted undiminished  in 
all  directions,  and  acts  at 
right  angles  to  all  sur- 
faces. 

310.  The  Hydraulic 
Elevator.  —  The  hydrau- 
lic elevator  (Figure  288) 

FIGURE  288.—  THE  HYDRAULIC  ELEVATOR,      uses    the     principle    ex- 


262 


MECHANICS   OF   FLUIDS 


pressed  by  Pascal's  Law.  A  large  piston  (P)  on  the  bottom 
of  the  elevator  fits  into  a  cylinder  in  the  ground.  A  pipe 
( K)  runs  down  the  side  of  the  cylinder  and  enters  it  at  the 
bottom. 

To  go  up,  the  stopcock  (S)  is  turned  so  that  water  enters 
the  pipe  (K)  from  the  water-main  (a).  The  water  flows 
down  the  pipe  ( K)  and  into  the  cylinder,  pushing  up  on  the 
piston  (P).  Since  the  pressure  in  the  water-main  is  about 
60  Ib.  per  square  inch,  there  is  also  a  pressure  of  60  Ib.  per 
square  inch  exerted  on  the  bottom  of  the  piston. 

If  this  piston  contains  100  sq.  in.,  the  elevator  will  be 
pushed  up  with  a  force  of  60  X  100  =  6000  Ib. 

To  come  down,  the  stopcock  is  turned  so  that  no  more 
water  can  get  into  the  pipe,  but  the  pipe  is  opened  to  the 
outlet  or  sewer.  The  weight  of  the  ele- 
vator pushes  the  water  out,  and  the 
elevator  comes  down  slowly. 

311.  Breaking   Jugs  or  Fruit  Jars.  — 
Jugs  and  fruit  jars  are  very  often  broken 
by  filling  them  with  a  liquid   and  then 
forcing  in  the  stopper  or  pressing  on  the 
lid.     The  force  is  applied  to  a  small  area, 
and  this  produces  a  large  pressure.     This 
pressure   being  transmitted  to  the  total 
area  of  the  sides  and  bottom  is  sufficient 
to  break  the  jar. 

312.  A  Liquid  in  an  Open  Vessel.  — 
FIGURE  289.  — PRES-   When  a  liquid  is  in  an  open  vessel,  the 

SURE     IN     AN     OPEN  .  . 

VESSEL.  pressure  acts  in  all  directions,  just  as  in 

the  closed  vessel,  but  the  amount  of 
pressure  depends  on  the  weight  of  the  liquid  above,  and 
not  on  an  outside  force. 


A   LIQUID  IN   AN  OPEN   VESSEL 


263 


Figure  289  shows  water  in  a  rectangular  tank  2  ft.  square  and  6  ft. 

deep.     It  is  seen  that  the  total  weight  of  the  water  rests  on  the  bottom. 

Since  water  weighs  62^  Ib.  per  cubic  foot,  the  force  on  the  bottom  is 

2  x  2  X  6  =  24  cu.  ft. 
24  X  62|  =  1500  Ib. 

Since  the  1500  Ib.  is  on  4  sq.  ft., 

1500 

Pressure  = =  375  Ib.  per  square  foot, 

4 

375' 

or  Pressure  =  -  -   =  2.6  Ib.  per  square  inch.        / 
144 

It  has  been  proven  that  the  pressure  on  the  bottom  of  a 
vessel  has  nothing  to  do  with  the  shape  of  the  vessel,  but 
depends  solely  upon  the  depth  of 
the  liquid  and  the  area  of  the 
base. 

Problem:  Find  the  pressure  on  the 
bottom  of  the  irregular  vessel  rilled 
with  water.  (Figure  290.) 

Assume  a  column  of  water  6  ft. 
high  standing  on  a  base  one  foot 
square. 

Then  its 
weight  =  1  X  1  X  6  X  62|  =  375  Ib. 

Thus  the  pressure  is  375  Ib.  per 
square  foot,  regardless  of  the  shape  of 
the  vessel. 

—  =  2.6  Ib.  per  square  inch. 
144 

Rule  :  To  find  the  pressure  in  pounds  per  square  foot  of  a 
liquid  in  an  open  vessel,  multiply  the  height  (h)  in  feet,  by  the 
weight  of  the  liquid  per  cubic  foot  (D). 


FIGURE  290.  —  PRESSURE  IN  AN 


IRREGULAR 
VESSEL. 


SHAPED       OPEN 


P  =  h-D. 


264  MECHANICS   OF   FLUIDS 

If   the   pressure   is   wanted   in  pounds  per  square  inch, 
divide  by  144. 

h-D 


P  = 


144 


Problem :  What  is  the  pressure  in  pounds  per  square  inch  20  ft. 
below  the  surface  of  water  ? 


144 

P  = — =  8.68  pounds  per  square  inch. 

144 

Problem:  What  is  the  pressure  3  ft.  under  mercury,  if   it  is  13.6 
times  as  heavy  as  water  ? 

P  =*J?. 
144* 

D      3  X  62.5  X  13.6 

P  =  -     —  -  =    17.7  pounds   per  square  inch. 

J.TX 


Problems 

1.  The  water  in  a  tank  stands  18  ft.  above  a  faucet.     What  is  the 
pressure  at  the  faucet? 

2.  How  high  does  the  water  rise  in  the  spout  of  a  teakettle? 

3.  Could  a  large  tank  of  water,  on  a  level  with  the  second  story,  and 
a  hose,  be  used  to  fight  fire  on  the  third  story  ?     Why  ?     - 

4.  What  is  the  pressure  on  a  deep-sea  diver  when  he  goes  down 
180  ft.,  if  sea  water  is  1.1  times  as  heavy  as  fresh  water? 

5.  What  is  the  pressure  at  a  faucet  on  the  third  floor,  if  the  pressure 
in  the  water-main  in  the  basement  45  ft.  below  is  60  Ib.  per  square  inch  ? 

313.  Air-Pressure.  —  Air,  like  water,  has  weight,  but  not 
so  great  as  water.  The  atmosphere  is  estimated  to  reach 
from  300  to  400  miles  above  the  surface  of  the  earth ;  and 
all  this  great  weight  of  air  above  is  resting  on  the  lower 
layers,  producing  a  pressure  just  as  the  weight  of  the  water 
above  produces  a  pressure  on  the  water  beneath. 


THE  SIMPLE  BAROMETER 


265 


At  sea-level  the  air-pressure  is  normally  14.7  Ib.  per  square 
inch.  Places  above  sea-level  have  less  pressure,  because 
there  are  fewer  layers  of  air  resting  on  them.  The  upper 
layers  are  not  so  heavy,  since  they  are  less  compressed, 
consequently  the  pressure  falls  rapidly 
as  you  rise  above  sea-level. 

The  air-pressure  is  measured  by  an 
instrument  called  the  barometer. 

314.  The  Simple  Barometer.  —  A 
simple  barometer  may  be  constructed  in 
this  way  :  Take  a  glass  tube  about  32  in. 
long,  closed  at  one  end,  and  fill  it  with 
mercury.  Then  invert  it  in  a  cup  of 
mercury,  being  careful  not  to  let  in  any 
air.  (Figure  291.) 

The  mercury  will  fall  away  from  the  top 
of  the  tube,  and  stand  at  30  in.,  more  or 
less,  according  to  the  air-pressure.  The 
space  above  the  mercury  in  the  tube  is 
almost  a  vacuum,  since  there  is  nothing 
in  it  except  a  little  mercury  vapor. 

The  pressure  of  the  mercury  in  the  tube 
is  exactly  balanced  by  the  pressure  of 
the  air  on  the  surface  of  the  mercury  in  the  cup.  This 
pressure  can  be  expressed  in  inches  of  mercury,  centimeters 
of  mercury,  pounds  per  square  inch,  or  grams  per  square 
centimeter. 

If  the  pressure  is  wanted  in  inches  of  mercury,  or  centimeters 
of  mercury,  it  is  read  directly  from  the  column  of  mercury ; 
but  if  it  is  wanted  in  pounds  per  square  inch,  or  grams  per 
square  centimeter,  it  has  to  be  calculated  as  one  calculates 
the  pressure  in  a  liquid. 


FIGURE  29  1.  —  THE 
SIMPLE  BAROMETER. 


266 


MECHANICS   OF   FLUIDS 


FIGURE  292. — THE   WEIGHT  OF  THE  AIR  MAKES  IT  POSSIBLE  TO  FLY. 

Example  :  What  is  the  pressure  in  pounds  per  square  inch,  when  the 
barometer  reads  28  in.  ? 

h  X  D 


144 

h  =  —  ft. 
12 

D  =  62.5  X  13.6  =  850  Ib.  per  cubic  foot. 
.    p  =  HX850  =  2|^850  =  13  „  ,b   per  square  inch 


144 


12  X  144 


315.  The  Commercial  Barometer.  —  The  commercial  ba- 
rometer, which  is  used  for  accurate  readings  of  the  air- 
pressure,  is  a  modified  form  of  the  simple  barometer. 

Figure  293  is  a  diagram  of  this  instrument.  The  glass 
tube  is  inclosed  in  a  brass  tube  having  part  of  it  cut  away 
so  that  the  glass  tube  can  be  seen  at  the  upper  end.  The 


THE  COMMERCIAL   BAROMETER 


267 


mercury  cup  has  a  rubber  or  leather  bottom,  so  that  it  can 
be  raised  or  lowered  by  a  set-screw  (a). 

A  small  movable  scale  (I7),  called  a  vernier,  is  operated 
by  a  set-screw  (b),  and  slides  at  the  side  of  a  scale  (S)  marked 
off  in  inches  and  tenths 
of  inches. 

To  make  a  reading : 
First,  adjust  the  mer- 
cury in  the  cup  with 
— V  the  set-screw  (a)  so  that 
the  top  of  the  mercury 
just  touches  the  point 
of  the  ivory  plug  (P). 
This  point  is  the  zero 
of  the  scale  (S). 

Second,  slide  the  ver- 
nier (V)  by  means  of 
screw  (6)  so  that  the 
bottom  of  the  vernier 
is  just  at  the  top  of 
the  mercury  in  the 
tube. 

Third,  read  the  scale 
(S)  and  the  vernier  (F). 
Figure  295  shows  an 
FIGURE  293. —  DIAGRAM   enlarged  drawing  of  the 


FIGURE    294.  — 
PHOTOGRAPH  OF 

%    '  A  BAROMETER. 

nier  (V). 

First,  note  where  the  zero  of  the  vernier  (V)  comes  on  the 
scale  (S).  In  the  figure  it- is  past  28.3,  and  not  quite  to  28 A ; 
then  the  scale  reading  is  the  smaller  of  these,  or  28.3. 

Second,  note  where  a  mark  on  the  vernier  (V)  coincides 


268 


MECHANICS   OF   FLUIDS 


with  a  mark  on  the  scale  (S).     In  the 
figure    it    is    5    on   the   vernier.     (It 
makes  no  difference  which  one  on  the 
scale.)       This    determines    the    next 
figure   to    be   annexed    to    the    scale 
reading,  which  makes  the  completed 
reading.     Thus  the  reading  in  Figure 
295  is  28.3  with  5  annexed,  or  28.35". 
316.   Weather      Maps.  —  Weather 
conditions    are    usually    accompanied 
by  certain  air-pressure  and  tempera- 
ture changes.     Knowing  this  fact,  the 
government  has  a  branch  of  the  De- 
partment   of    Agriculture    called    the 
United  States  Weather  Bureau,  part  of  whose  duties  it  is 
to  make  weather  maps  and  from  them  send  out  weather 
forecasts. 


FIGURE  295.  —  ENLARGED 
DRAWING  OF  THE  VER- 
NIER OF  A  BAROMETER. 


FIGURE  296.  — A  TYPICAL  WEATHER  MAP. 


THE  LIFT-PUMP 


269 


The  Weather  Bureau  has  stations  established  all  over 
the  United  States,  and  every  24  hours  these  stations  report 
to  the  head  office  at  Washington,  D.  C.,  on  the  weather 
conditions.  Some  of  the  things  reported  are  barometer 
reading  (reduced  to  normal  conditions),  temperature,  clear, 
cloudy,  rain,  or  snow,  direction  and  velocity  of  wind.  These 
reports  are  then  summarized  and  reported  back  to  all  the 
stations.  Each  station  then  draws  up  a  weather  map  and 
forecasts  the  local  weather  for  the  next  48  hours. 

A  weather  map  (Figure  296)  is  made  by  drawing  heavy 
lines,  called  isobars,  through  all  stations  of  equal  pressure ; 
dotted  lines,  called  isotherms,  through  all  stations  of  equal 
temperature  ;  an  arrow  at 
each  station,  indicating 
the  direction  of  the  wind ; 
and  small  circles  marked 
to  show  whether  it  is 
clear,  partly  cloudy,  cloudy, 
rain,  or  snow,  respectively. 
The  cloudy  areas  are 
shaded,  the  low  pressure 
areas  are  marked  "  LOW," 
and  the  high  pressure  areas 
are  marked  "  HIGH." 

For  a  further  study  of 
the  weather  map  read 
some  good  physical  geog- 
raphy. 

317.  The  Lift-Pump.  - 
Figure  296  is  a  diagram  of 
the  lift-pump,  which  is  an 
application  of  air-pressure.  FIGURE  297. —THE  LIFT-PUMP. 


270 


MECHANICS   OF   FLUIDS 


The  piston  (P)  works  air-tight  in  the  cylinder  of  the 
pump.  When  the  piston  is  drawn  up,  the  valve  (B)  closes, 
and  a  partial  vacuum  is  left  behind  the  piston.  The  air- 
pressure,  acting  on  the  surface  of  the  water  (C,  C)  in  the 
well,  forces  the  water  up  to  fill  this  partial  vacuum. 

On  the  down  stroke  of  the  piston,  valve  (A)  closes  and 
(B)  opens.  After  several  strokes,  the  water  reaches  up 
into  the  pump.  The  operation  is  continued,  and  the  water 
flows  through  the  valves,  instead  of  air.  When  the  water 
gets  high  enough,  it  runs  out  of  the  spout. 

Sometimes  the  pump  will  not  start,  but  has  to  be 
"  primed."  This  is  because  the  valves  or  piston  will  not 
hold  air,  so  water  has  to  be  put  in  to  make  them  air-tight. 

This  kind  of  pump  can  be  used  only  to  pump  water  from 
shallow  wells  and  cisterns,  since  the  air-pressure  will  raise 

water  only  34  ft. 
under  ideal  condi- 
tions ;  and  only 
about  28  ft.,  practi- 
cally. 

318.  The  Force- 
Pump.  —  The  force- 
pumps  used  to  drive 
water  into  mains, 
pressure  tanks,  and 
fire  hose  are  much 
like  the  lift-pump, 
only  instead  of  allow- 
ing the  water  to  flow  out  of  the  spout  of  its  own  accord,  it 
is  confined  in  the  top  of  the  pump  and  forced  out.  (Figure 
298.) 

An  air-chamber  (C)  is  attached  to  the  pump,  so  that  the 


FIGURE  298. — THE  FORCE-PUMP. 


OTHER  APPLICATIONS  OF  AIR-PRESSURE      271 


d 


air,  when  compressed,  acts  as  a  spring  to  keep  the  pump 
from  bursting  and  to  keep  the  water  flowing  between  strokes. 

319.  The    Siphon.  —  Figure    299    represents    a    siphon, 
which  consists  of  a  tube  with  its  ends  in  water,  at  different 
levels.     If  the  tube   is  completely  filled  with  liquid,   the 
liquid  will  run  through  the  tube  from  the  higher  level  to 
the  lower. 

The  air-pressure  on  the  surface  of  the  water  (c)  tends  to 
lift  the  water  34  ft.  in  the  tube.     Also  the  same  air-pressure 

at  (d)  tends  to  lift  the  x ^ 

water  34  ft.  on  the 
other  side  of  the  tube. 
But  the  water  presses 
downward  on  the  two 
sides  with  a  pressure 
of  a  ft.  and  b  ft.,  re- 
spectively. This 
leaves  a  pressure  of 
34  -  a  and  34  -  6, 
respectively.  Since  b 
is  greater  than  a,  the 
greater  pressure  is  to- 
wards (6),  and  the  water  runs  in  that  direction.  The 
greater  the  difference  in  (a)  and  (b),  the  faster  the  liquid 
will  flow. 

The  siphon  is  used  for  getting  acids  out  of  carboys,  cider 
out  of  barrels,  water  out  of  tanks,  etc. 

320.  Other  Applications  of  Air-Pressure.  —  Drawing  soda 
water  through  a  straw  could  not  be  done  if  it  were  not  for 
air-pressure.     The  air  is  drawn  out  of  the  straw,  leaving  a 
partial  vacuum,  and  the  air-pressure  forces  the  soda  water 
up  to  take  the  place  of  the  air. 


FIGURE  299.  — THE  SIPHON. 


272  MECHANICS   OF   FLUIDS 

Ordinary  breathing  depends  upon  air-pressure.  The 
muscles  of  the  chest  act  and  make  the  cavity  in  which  the 
lungs  are  located  larger.  This  reduces  the  pressure  in  the 
lungs,  and  the  air  is  forced  in  to  equalize  the  pressure. 

Fruit-jar  lids  are  often  hard  to  get  off  on  account  of  the 
pressure  of  the  air.  When  the  jar  is  sealed,  the  liquid 
and  air  in  the  jar  are  hot.  On  cooling,  they  both  contract, 
thus  reducing  the  pressure  inside  the  jar.  The  outside 
air-pressure  then  holds  the  lid  on  very  tight.  Corks 
drawn  into  bottles  in  the  same  way  are  often  hard  to  get 
out. 

Air-pressure  enables  the  house-fly  to  stick  to  the  ceiling. 
His  feet  have  tiny  pads  on  them,  and  when  he  sets  them 
down  all  the  air  is  squeezed  out  from  under  them,  and  then 
the  pressure  of  the  air  makes  them  stick  to  the  wall  or  ceil- 
ing. A  fly  will  fall  off  the  side  of  a  bell  jar  and  will  crawl 
around  on  the  bottom,  if  he  is  put  inside  and  the  air  is 
pumped  out. 

"  Suction  soles  "  on  gymnasium  shoes  are  similar  to  the 
foot-pads  of  the  fly.  The  soles  have  holes,  or  depressions, 
on  the  bottoms,  and  when  the  weight  of  the  wearer  comes 
down  on  them,  the  air  is  squeezed  out,  and  then  the  air- 
pressure  outside  tends  to  make  them  "  stick."  "  Suction 
tread  "  tires  work  on  exactly  the  same  principle. 

321.  Boyle's  Law.  —  All  gases  can  be  compressed  by 
putting  pressure  on  them.  That  is,  more  and  more  gas  may 
be  forced  into  the  same  space,  or  a  certain  amount  of  gas 
may  be  forced  into  a  smaller  space.  In  either  case  the 
pressure  in  the  gas  is  increased. 

On  the  other  hand,  a  gas  will  expand  if  allowed  space  to 
do  it  in.  In  this  case  the  pressure  is  decreased. 

Boyle  stated  these  facts  in  a  law,  called  Boyle's  Law. 


SURFACE   TENSION  273 

The  volume  of  a  gas  at  a  constant  temperature  varies  in- 
versely as  the  pressure  exerted  upon  it. 

This  means  that  if  the  pressure  is  doubled,  the  volume  is 
halved;  or  if  the  pressure  is  halved,  the  volume  is  doubled, 
etc. 

The  law  applies  to  natural  or  artificial  gas  used  as  a  fuel. 
The  higher  the  pressure,  the  more  gas  there  is  squeezed  into 
a  cubic  foot ;  and,  since  gas  is  usually  sold  by  the  cubic  foot, 
the  pressure  affects  the  cost  of  the  gas. 

This  change  in  cost  due  to  change  in  pressure  is  not  as 
great  as  some  people  think.  An  illustration  will  show  how 
much  the  effect  is. 

Suppose  the  normal  pressure  is  6  oz.  per  square  inch. 
(This  is  the  average  pressure  maintained  for  natural  gas.) 
This  means  6  oz.  per  square  inch  above  atmospheric  pres- 
sure. Since  atmospheric  pressure  is  about  14.5  lb.,  or  232 
oz.,  per  square  inch,  this  makes  the  actual  pressure  in  the 
gas  main  232  +  6  =  238  oz.  per  square  inch. 

Now,  if  the  gas  pressure  should  fall  50  per  cent,  or  to  3  oz. 
above  atmospheric  pressure,  the  actual  pressure  in  the  main 
would  be  238  —  3  =  235  oz.  per  square  inch. 

235 
Thus  there  will  be  -   -  as  much  gas  in  a  cubic  foot  as 

there  was  at  the  normal  pressure  of  6  oz.  per  square  inch. 

The  inflation  of  tires  with  air  under  pressure  is  also  an 
application  of  Boyle's  Law. 

322.  Surface  Tension.  —  All  liquids  act  as  if  they  have  a 
"  skin  "  or  "  membrane  "  stretched  over  their  surfaces.  A 
needle  may  be  laid  on  the  surface  of  water  (Figure  300),  if 
care  is  taken.  The  surface  of  the  water  is  curved  under  the 
needle  just  as  if  there  were  a  cover  over  the  water.  This 
apparent  "  skin  "  or  membrane  is  called  surface  tension. 


274 


MECHANICS   OF   FLUIDS 


The  fact  is,  there  is  no  membrane  on  the  liquid.     The 
molecules  at  the  surface  are  exactly  the  same  as  inside  the 

liquid.     Surface    tension    is    ex- 
plained as  follows : 

Consider  a  molecule  of  water 


FIGURE  300.  — A  NEEDLE 
LYING  ON  WATER, 


FIGURE  301. — •  SURFACE 
TENSION  EXPLAINED. 


(M,  Figure  301)  at  the  surface  of  the  water, 
in  quadrants  (a)  and  (d) 
attracts  the  molecule  (m) 
and  tends  to  pull  it  down- 
ward. As  there  is  no 
water  in  (b)  and  (c),  — 
but  only  air,  which 
attracts  the  molecule  (m) 
but  slightly,  —  the  result- 
ing effect  is  for  the  mole- 
cule (m)  to  be  pulled 
toward  the  center  of  the 
water,  and  every  other 
molecule  on  the  surface 
pulled  toward  the 


The  water 


is 


center  in  the  same  way. 


FIGURE  302. — WATER  IN  CONTACT  WITH 
GLASS. 


CAPILLARITY 


275 


This  gives  the  effect  of  a  stretched  covering  over  the  surface 
of  the  liquid. 

323.  Capillarity.  —  Capillarity  is  an  application  of  sur- 
face tension.  Figure  302  shows  water  in  contact  with  glass. 
The  water  against  the  glass 
is  curved  up  ;  because 
glass  has  a  greater  attrac- 
tion for  water  than  water 
has  for  water;  therefore 
the  glass  in  quadrant  (c) 
pulls  the  molecule  of  water 
(m)  more  than  the  water 
in  quadrant  (a).  Also  the 
glass  in  (6)  pulls  (m)  more 
than  does  the  air  in  (d). 
This  makes  the  surface  of 
the  water  curve  as  shown 


in  the  figure. 


FIGURE  303.  —  MERCURY  IN  CONTACT 
WITH  GLASS. 

Figure   303   shows  mer- 

cury in  contact  with  glass.  The  mercury  against  the  glass 
is  curved  down.  Mercury  attracts  mercury  more  than 
glass  attracts  mercury,  therefore  the  mercury  in  quadrant 
(a)  pulls  the  molecule  of  mercury  (m) 
more  than  the  glass  in  quadrant  (c). 
Also  the  glass  in  (6)  attracts  (m)  more 
than  the  air  in  (d).  Thus  the  sur- 
face curves  downward  as  shown  in  the 
figure. 

When  a  tube  is  put  into  a  vessel  of 
water,  the  water  creeps  up  the  tube,  as 


A  GLASS  TUBE.          put  into  a  vessel  of  mercury,  the  mercury 


276 


MECHANICS   OF   FLUIDS 


creeps   down    the   tube.       (Figure    305.)      This    is    called 

capillarity. 

The  steps  in  this  process  are  as  follows : 

When  the  tube  is  placed 
in  the  water  (Figure  304), 
the  surface  of  the  water 
curves  up  the  glass;  but 
since  the  surface  tension  on 
the  water  acts  like  a  rubber 
covering,  the  surface  straight- , 
ens  out;  and  then  curves 
again.  This  alternation  is 
kept  up  until  the  weight  of 
water  in  the  tube  is  so  great 
that  the  surface  tension  is 
not  able  to  lift  it  and 
straighten  out  the  surface. 

In  the  case  of  mercury  and 
glass  the  mercury  is  pressed 
down  (Figure  305),  the  pro- 
cess being  the  same  as  for 
water,  except  that  the  sur- 
face curves  in  the  opposite 
direction. 

324.  Other  Applications  of 
Surface  Tension.  —  Rain- 
drops become  spherical  on 

account  of  surface  tension.     The  elastic  surface  tends  to  pull 

all  molecules  towards  the  center,  thus  producing  a  sphere. 
Drops  of  water  on  a  greased  surface  become  spherical  for 

the  same  reason.     Similarly,  drops  of  mercury  on  a  table  or 

your  hand  become  spherical. 


\ 


FIGURE  305. — How  MERCURY  CREEPS 
DOWN  A  GLASS  TUBE. 


ARCHIMEDES'   PRINCIPLE 


277 


Soap-bubbles  are  thin  films  of  soapy  water  with  a  double 
surface  tension  —  one  on  the  inside,  and  one  on  the  outside. 
Sometimes  you  can  see  the  water  run  down  between  the 
two  surfaces. 

The  fact  that  the  white  of  an  egg  has  a  high  surface  tension 
makes  it  possible  to  "  beat  "  it  into  a  white  fluffy  mass. 
This  fluffy  mass  is  made  up  of  thousands  of  tiny  bubbles 
which  depend  on  surface  tension  for  their  existence. 

Oil  is  sometimes  poured  on  stormy 
seas  to  stop  the  breaking  of  the 
waves  and  thus  save  the  ship.  The 
three  surface  tensions  act  as  a 
blanket  over  the  water.  Explain 
why  there  are  three  surface  tensions. 

325.   Archimedes'      Principle.  - 
Archimedes  formulated  the  follow- 
ing principle  : 

A  body  immersed  in  a  fluid  loses  in 
weight  an  amount  equal  to  the  weight 
of  the  fluid  displaced. 

This  principle  can  be  demon- 
strated as  follows  :  Suppose  a  cube 
1  ft.  on  an  edge  be  immersed  in  water  so  that  the  top  of 
the  cube  is  5  ft.  below  the  surface.  (Figure  306.)  Then 
the  bottom  of  the  cube  is  6  ft.  below  the  surface.  The  force 
downward  on  the  top  of  the  cube  equals 


FIGURE  306.- — ARCHIMEDES' 
PRINCIPLE  VERIFIED. 


h-  D-A 

5  X  62^  X  1  = 


Ib. 


The  force  upward  on  the  bottom  of  the  cube  equals 


F  =  h'D-A 
F  =  6  X  62£  X  1 


375  Ib. 


278  MECHANICS   OF   FLUIDS 

This  leaves  a  force  upward  of  375  -  31 2i  Ib.  =  62^  Ib. 
But  62^  Ib.  is  the  weight  of  a  cubic  foot  of  water,  which  is 
also  the  volume  of  the  cube. 

The  illustration  above  assumed  that  the  body  was  com- 
pletely submerged.  If  the  weight  of  the  body  is  less  than 
the  weight  of  an  equal  volume  of  liquid,  then  the  body  will 
sink  to  a  depth  where  it  displaces  a  weight  of  liquid  equal 
to  the  weight  of  the  body. 

For  example,  if  a  body  of  one  cubic  foot  weighs  40  Ib.,  it 

will  sink  in  water  until  it  displaces  40  Ib.  of  water,  or  

cu.  ft. 

Thus  a  body  heavier  than  a  liquid  sinks,  and  one  lighter 
than  a  liquid  floats. 

326.  Applications   of  Archimedes'   Principle.  —  A   stone 
submerged  in  water  is  much  easier  to  lift  than  one  out  of 
water. 

A  person  in  water  weighs  very  little.  This  makes  swim- 
ming possible.  Why  does  the  swimmer  keep  as  much  of 
his  body  under  water  as  possible  ? 

An  egg  will  sink  in  fresh  water  but  will  float  in  salt  water. 
Explain. 

Grapefruit  and  oranges  may  be  tested  for  juiciness  by 
dropping  them  into  water.  If  they  are  juicy  and  heavy,  they 
will  float  very  low  in  the  water,  but  if  dry  and  light,  they  will 
float  high. 

A  ship  sinks  in  water  until  the  weight  of  the  water  dis- 
placed equals  the  weight  of  the  ship  and  its  cargo.  That  is 
the  reason  why  an  empty  freighter  rides  high  and  a  loaded 
one  rides  low  in  the  water. 

327.  Density  and  Specific  Gravity.  —  The  term   density 
means  the  mass  per  unit  volume.     A  cubic  foot  of  water 


PROBLEMS  279 

contains  G2|  lb.,  and  a  cubic  centimeter  contains  1  gram. 
Therefore  the  density  of  water  is  62|  lb.  per  cubic  foot,  or  1 
gram  per  cubic  centimeter. 

Specific  gravity  is  the  ratio  of  the  mass  of  a  body  to  the  mass 
of  an  equal  volume  of  water. 

P       .  -  .  mass  of  body 

specific  gravity  = 


mass  of  equal  vol.  of  water' 

Specific  gravity  is  a  comparison  of  the  density  of  a  body 
to  the  density  of  water. 

Since  the  density  of  water  in  the  metric  system  is  nu- 
merically 1  (1  gram  per  cubic  centimeter),  the  specific  grav- 
ity and  the  density  of  a  body  in  that  system  are  numerically 
equal. 

By  the  use  of  the  table  on  the  next  page  the  weight  of  any 
certain  volume  of  a  substance  can  be  found,  or  the  volume 
of  any  certain  weight  can  be  found. 

Example  :  What  is  the  weight  of  25  cu.  ft.  of  copper  ? 
From  the  table  :       1  cu.  ft.  copper  =  550.6  lb. 

25  cu.  ft.  =  25  X  550.6  =  13765  lb. 

Example  :  What  is  the  volume  of  1000  lb.  of  cast  iron  ? 
From  the  table  :     1  cu.  ft.  cast  iron  =  449  lb. 

2.23  cu.  ft. 


449 

Problems 

1.  What  is  the  weight  of  a  cedar  chest  that  is  made  of  2  cu.  ft.  of 
lumber  ? 

2.  If  a  gold  chain  weighs  30  grams,  how  many  cubic  centimeters  of 
gold  does  it  contain  ? 

3.  Why  is  cork  used  in  life  preservers  ? 

4.  A  gallon  contains  231  cu.  in.,  and  a  cu.  ft.  contains  1728  cu.  in. 
What  is  the  weight  of  a  gallon  of  water  ? 


280 


MECHANICS    OF    FLUIDS 


TABLE    OF    DENSITIES  AND  SPECIFIC  GRAVITIES  OF  SOME 
SUBSTANCES 


•j 

DENSITY 

. 

SUBSTANCE 

Lb.  per 
Cu.  Ft. 

Gms.  per  c.c. 

SPECIFIC  GRAVITY 

Ash  (dry)    .     .     .     . 

43.7 

.70 

.70 

Ash  (green) 

52.8 

.84 

84 

Acetic  Acid     
Alcohol       ...... 

66.4 
50.0 

1.062 
.80 

1.062 
.80 

Aluminum 

165.6 

2.65 

265 

Beech     ........ 
Cedar     

53.2 
35.0 

.69  to  .852 
.561 

.69  to  .852 
.561 

Cork      . 

15.0 

24 

24 

Copper  (cast)       .... 
Copper  (sheet)     .... 
Brass 

550.6 
555.0 
527  5 

8.81 
8.88 
8  38  to  8  44 

8.81 
8.88 
8  38  to  8.44 

Gold 

12188 

19  50 

19  50 

Hydrochloric  Acid    . 
Iron  (wrought)    .... 
Iron  (cast) 

75.2 
480-0 
449  0 

1.22 
7.68 
720 

1.22 
7.68 
720 

Lead       ,'    . 
Maple    ...               . 

709.6 
460 

11.36 
75 

11.36 
75 

Mercury 

8500 

136 

136 

Milk       ....... 

64  5 

1.032 

1.032 

Nitric  Acid 

763 

1  22 

1.22 

Oak  

53.1 

.85 

.85 

Pine       
Platinum    

28.8 
13488 

.46 
21  5 

.46 
21.5 

Sea  Water       .                    , 

644 

1  03 

1  03 

Silver     . 

656  3 

10  5 

105 

31  2 

5 

.5 

Steel       

5900 

784 

7.84 

Sulphuric  Acid     .... 
Tin  (cast)        

115.1 
4558 

1.84 
729 

1.84 
7.29 

Walnut       .... 

41  6 

67 

.67 

Water     . 

62  5 

1  00 

1.00 

Zinc  " 

431  3 

69 

69 

METHODS   OF   FINDING  SPECIFIC  GRAVITY      281 

5.  If  there  were  12  cubes  of  gold,  1  in.,  2  in.,  3  in.,  etc.,  on  an  edge 
respectively,  and  you  were  told  you  could  have  whichever  one  you 
could  lift  at  the  first  trial,  which  one  would  you  try?     Why? 

6.  If  a  bucket  containing  water  is  placed  on  the  platform  of  a  set  of 
scales  and  is  found  to  weigh  40  lb.,  what  weight  will  the  scales  show  if 
a  cast  iron  cube  3  in.  on  an  edge  is  supported  just  under  the  surface  of 
the  water  by  a  string,  care  being  taken  that  the  cube  does  not  touch 
the  bucket? 

7.  How  could  you  find  the  cubical  contents  of  an  egg? 

8.  From  the  table  determine  the  order  of  the  heaviest  substances 
named. 

328.  Methods  of  Finding  Specific  Gravity.  —  (1)  If  it  is 
possible  to  weigh  a  body  and  also  to  determine  its  volume, 
the  density  can  be  found  by  dividing  the  weight  by  the  volume. 
If  the  body  can  be  weighed  and  the  dimensions  taken,  then 
the  weight  divided  by  the  volume  gives  the  density.  This 
density  divided  by  the  density  of  water  gives  its  specific 
gravity. 

Example  :  What  is  the  specific  gravity  of  a  piece  of  metal  if  it  weighs 
40  lb.,  and  is  2"  X  4"  X  12"? 
Solution  : 

2  X  4  X  12  =  96  cu.  in. 
96         1 


40 

7  =  40  X  18  =  720  lb.  per  cubic  foot. 

fl 

Density  of  water  =  62.5  lb.  per  cubic  foot. 

720 
/.     —  -  11.5  =  sp.gr. 

(2)  The  hydrometer  (Figure  307)  is  an  instrument  used 
to  determine  the  specific  gravity  of  liquids.  It  is  a  tube, 
weighted  at  the  bottom,  that  has  a  scale  marked  on  the  side. 
The  depth  to  which  it  sinks  gives  the  specific  gravity  reading. 


282 


MECHANICS   OF   FLUIDS 


An  hydrometer,  made  to  read  the  specific  gravities  of  liquids 
lighter  than  water,  has  the  zero  of  the  scale  at  the  bottom,  but 

one  for  liquids  heavier  than  water 
has  the  zero  at  the  top.  Why? 
(3)  Another  method  for  find- 
ing the  specific  gravity  of  a 
body,  and  the  one  generally 
used  if  the  body  is  irregular  in 
shape,  is  to  weigh  the  body  in 
air,  and  then  in  water.  The 
difference  represents  the  weight 
of  the  water  displaced.  Why? 
Then  the  weight  in  air  divided 
by  the  loss  in  weight  equals 
specific  gravity. 

Example :  What  is  the  specific 
gravity  of  a  body  which  weighs  19 
grams  in  air  and  12  grams  in  water? 

Solution  : 


FIGURE  307. — THE  HYDROM- 
ETER. 


19  -  12  =  7   grams,    wt.   of  water 
displaced. 

1Q 

^=2.71=  sp.gr. 

(4)  Other  cases :  (a)  If  the  body  is  lighter  than  water,  a 
sinker  must  be  used ;  but  the  principle  is  similar. 

(6)  If  the  object  is  soluble  in  water,  it  can  be  weighed  in  a 
liquid  in  which  it  is  not  soluble,  but  whose  specific  gravity 
is  known. 

(c)  If  it  is  a  liquid  whose  specific  gravity  is  to  be  found,  a 
sinkter,  first  weighed  in  air,  then  in  water,  and  then  in  the 
liquid,  will  give  the  data  necessary  for  finding  the  specific 
gravity. 


REVIEW  PROBLEMS  283 

Explain,  with  an  example,  how  to  find  the  specific  gravity  in  (a), 
(6),  and  (c). 

Problems 

1.  What  is  the  density  and  specific  gravity  of  a  piece  of  butter 
which  is  2|"  X  2£"  X  4"  and  weighs  1  Ib.  ? 

2.  What  is  the  specific  gravity  of  an  egg,  if  it  weighs  1  oz.  in  air  and 
.1  oz.  in  water? 

3.  What  is  the  specific  gravity  of  a  grapefruit,  if  the  following  data 
are  taken  ?     Weight  of  grapefruit  in  air,  with  a  sinker  attached,  but  in 
water,  equals  1.5  Ib. ;    weight  of  sinker  alone  in  water  equals  .3  Ib. ; 
weight  of  grapefruit  in  water  with  sinker  attached  and  in  water  equals 
.lib. 

4.  What  is  *the  specific  gravity  of  a  crystal  of  a  substance,  if  it 
weighs  .24  gram  in  air,  and  .05  gram  in  a  liquid  whose  specific  gravity 
is  1.5? 

5.  What  is  the  specific  gravity  of  a  liquid,  if  a  sinker  weighs  12  grams 
in  air,  5  grams  in  the  liquid,  and  4  grams  in  water? 

Review  Problems 

1.  Define  force,  work,  mechanical  advantage,  and  efficiency. 

2.  Classify  and  describe  levers. 

3.  If  a  force  of  15  Ib.  is  exerted  on  the  handles  of  a  nutcracker  6 
inches  from  the  pivot  when  the  nut  is  placed  1|  inches  from  the  pivot, 
what  is  the  pressure  on  the  nut? 

4.  The  crank  on  an  awning  lifter  is  15  inches  long,  and  the  radius 
of  the  axle  on  which  the  rope  is  wound  is  1  inch.     What  force  on  the 
crank  is  necessary  to  lift  the  awning  if  it  pulls  down  on  the  rope  with 
a  weight  of  50  Ib.  ? 

5.  If  a  piano  weighs  600  Ib.  and  is  rolled  up  a  plank   16  ft.  long 
into  a  truck  4  ft.  high,  what  force  is  necessary,  ignoring  friction  ? 

6.  How  fast  will  the  blades  of  an  egg-beater  run,  if  the  handle  is 
fastened  to  a  wheel  with  50  cogs,  which  in  turn  drives  a  wheel,  with 
8  cogs,  directly  connected  to  the  blades,  the  handle  being  turned  96 
R.  P.  M.? 

7.  What  horsepower  is  exerted  when  a  120-lb.  girl  climbs  a  stairs 
15  ft.  high  in  \  min.  ? 

8.  Define  motion. 


284  MECHANICS  OF   FLUIDS 

9.   What  are  Newton's  three  laws  of  motion? 

10.  Explain  the  use  of  the  parallelogram  of  force. 

11.  How  far  will  a  train  travel  in  10  seconds  if  it  has  an  accelera- 
tion of  |  ft.  per  second,  per  second,  and  starts  from  rest? 

12.  How  long  will  it  take  a  stone  to  fall  100  ft.  ? 

13.  How  far  will  an  automobile  coast  if  it  has  a  velocity  of  36  ft. 
per  second  and  slows  down  at  the  rate  of  2  ft.  per  second,  per  second  ? 

14.  What  is  the  apparent  weight  of  a  girl  going  up  in  an  elevator 
which  is  increasing  its  speed  at  the  rate  of  3  ft.  per  second,  per  second, 
if  her  actual  weight  is  110  Ib.  ? 

15.  Give  two  uses  of  the  pendulum. 

16.  Explain  why  gases  and  liquids  can  be  delivered  through  pipes 
while  solids  cannot. 

17.  How  does  force  on  a  surface  differ  from  pressure  on  a  surface? 

18.  What  is  the  pressure  in  pounds  per  square  inch  at  the  bottom 
of  a  tank  of  water  8  ft.  deep  ? 

19.  If  the  water  main  pressure  is  60  Ib.  per  square  inch,  how  high 
will  the  water  rise  in  a  pipe? 

20.  Why  do  high  buildings  have  ext  a  pumping  systems  of  their 
own? 

21.  If  you  were  to  supply  water  to  a  house,  from  an  open  tank,  where 
would  you  locate  the  tank  ? 

22.  Give  five  applications  of  air-pressure. 

23.  Explain  capillarity. 

24.  State  Archimedes'  principle. 

25.  What  is  meant  when  we  say  the  specific  gravity  of  brass  is  8.3  ? 

26.  Why  will  an  egg  sink  in  fresh  water  and  float  in  salt  water  ? 

27.  How  could  you  test  a  grapefruit  for  juiceness  in  a  simple  manner  ? 

28.  What  is  the  specific  gravity  of  an  egg,  if  it  weighs  1.1  oz.  in 
air,  and  .08  oz.  in  water  ? 


APPENDIX 


I.   Freezing  and  Boiling  Points  of  Some  Common  Substances 
Under  Normal  Atmospheric  Pressure 


SUBSTANCE 

FREEZING  POINT 

BOILING  POINT 

Oxygen 

Centigrade 

-  235° 

Centigrade 
-  189° 

Ammonia     
Ether  

-    75° 
-  113° 

-    39° 
35° 

Methylic  Alcohol 

-  112° 

66° 

Distilled  Water     
Acetic  Acid  

0° 
-    17° 

100° 
117° 

Turpentine 

-    27° 

157° 

Fat,  Oil,  etc  
Mercury  

-    33° 

-    388° 

210° 
357° 

II.    Vapor  Tension  of  Water 

Temperatures  Given  in  Centigrade  Degrees,  and  Vapor  Tension  in 
Centimeters  of  Mercury 


TEMPERATURES 

VAPOR  TENSIONS 

TEMPERATURES 

VAPOR  TENSIONS 

-  10 

.22 

3 

.57 

-  9 

.23 

4 

.61 

-  8 

.25 

5 

.65 

-  7 

.27 

6 

.70 

-  6 

.29 

7 

.75 

-  5 

.32 

8 

.80 

-  4 

.34 

9 

.86 

-  3 

.37 

10 

.92 

-  2 

.39 

11 

.98 

—  1 

.42 

12 

1.05 

0 

.46 

13 

1.12 

1 

.49 

14 

1.19 

2 

.53 

15 

1.27 

285 


286 


HOUSEHOLD  PHYSICS 
II.   Vapor  Tension  of  Water  —  Continued 


TEMPERATURES 

VAPOR  TENSIONS 

TEMPERATURES 

VAPOR  TENSIONS 

16 

1.35 

30 

3.15 

17 

1.44 

31 

3.34 

18 

1.54 

32 

3.54 

19 

1.63 

33 

3.74 

20 

1.74 

34 

3.96 

21 

1.85 

35 

4.18 

22 

1.97 

36 

4.42 

23 

2.09 

37 

4.67 

24 

2.22 

38 

4.93 

25 

2.35 

39 

5.20 

26 

2.51 

40 

5.49 

27 

2.65 

41 

5.79 

28 

2.81 

45 

7.14 

29 

2.98 

100 

76.00 

III.   Table  of  Specific  Heats  of  Some  of  Our  Most  Common  Substances 
SUBSTANCE  SPECIFIC  HEAT 

Aluminum 22 

Brass 094 

Copper .095 

Iron 1138 

Mercury 038 

Lead .031 

Ice 5 

Air  (at  constant  pressure) 2375 

Hydrogen  (at  constant  pressure)  ......     3.4 

Steam  (at  constant  pressure) 48 

IV.   Table  of  Coefficients  of  Linear  Expansion 


SUBSTANCES  COEFFICIENT 

Aluminum 0000222 

Brass 0000187 

Copper 000017 

Glass  .0000083 


SUBSTANCES  COEFFICIENT 

Iron     .     .  .0000112 

Platinum .  .0000088 

Steel    .     .  .000013  (tempered) 

Steel    .     .  .000011  (untempered) 

If  the  range  in  temperature  is  given  in  Fahrenheit  degrees,  then  the 
above  coefficients  must  be  multiplied  by  -jj-. 


APPENDIX 
V.    Sources  of  Heat 


287 


MATERIAL 

KIND 

HEAT  VALUE 

Coal  

Wood  
Gas 

[Hard 
|  Soft 
I  Coke 
Hard 
Soft 
Natural 

14000  B.  T.  U.'s  per  Ib. 
12000  B.  T.  U.'s  per  Ib. 
14000  B.  T.  U.'s  per  Ib. 
8400  B.  T.  U.'s  per  Ib. 
8600  B.  T.  U.'s  per  Ib. 
1200  B.  T.  U.'s  per  cu.  ft. 

Oils  
Electricity  . 

Artificial 
(  Kerosene 
{  Naphtha 
[  Crude  Oil 

600  B.  T.  U.'s  per  cu.  ft. 
20000  B.  T.  U.'s  per  Ib. 
20000  B.  T.  U.'s  per  Ib. 
18000  B.  T.  U.'s  per  Ib 
3411.72  B.  T.  U.'s  per  kw.  hr. 

(Electricity  is  given  in  this  table,  though  it  is  not  a  fuel.) 
VI.   Heat  Value  of  Foods 


FOOD  (edible  portion) 

APPROXIMATE  MEASURE  OP 
1  00-G  HEAT-CALORY 
PORTION 

WEIGHT  IN 
OUNCES  OP 
100-GREAT- 
CALORY 
PORTION 

Almonds    

15  average  

0.5 

Apples 

2  medium            .... 

6.5 

Apricots  fresh 

2  large 

6  1 

Asparagus,  cooked  .... 
Bacon,  smoked  (uncooked)   . 
Bananas     

2  servings  
1  thin  slice,  small    .     .     . 
1  large 

7.5 
0.6 
3.6 

Beans,  baked,  canned  .     .     . 
strin^  canned 

1  small  serving  (^  cupful) 
5  servings 

2.8 
17.2 

lima  canned 

1  large  side-dish           . 

46 

Beef  corned 

1  2 

dried   salted  and  smoked 

4  large  slices 

20 

porterhouse  steak 

1  small       

1.3 

ribs  lean 

1  average  serving    . 

1.9 

ribs   fat 

09 

round,  free  from  visible  fat 
rump  lean 

1  generous  serving  .     .     . 

3.1 

1  7 

rump  fat;    

0.9 

sirloin  steak 

1  average  serving    . 

1.4 

288 


HOUSEHOLD  PHYSICS 


VI.    Heat  Value  of  Foods  —  Continued 


FOOD  (edible  portion) 

APPROXIMATE  MEASURE  op 
IOO-GREAT-CALORY 
PORTION 

WEIGHT  IN 
OUNCES  OF 
IOO-GREAT- 
CALORY 
PORTION 

Beets  cooked 

3  servings                             .     * 

89 

Brazil  nuts     .... 

3  average  size  ...... 

0.5 

Bread,  graham    . 

1  thick  slice      .          .... 

1.3 

toasted 

2  medium  slices  (baker's) 

1  2 

white  homemade 

1  medium  slice      

1.3 

average  

1  thick  slice      ...... 

1.3 

whole-wheat 

1  thick  slice                           .     . 

1.4 

Buckwheat  flour 

T  cupful  . 

1.0 

Butter  

1  tablespoonful  (ordinarv  pat) 

0.5 

Buttermilk     .... 
Cabbage 

lj  cupfuls  (1^  glasses)     .     .     . 
2  servings                           •  .     . 

9.9 
11  2 

Calf's  foot  jellv  .     .     . 

4.1 

Carrots,  fresh      .     .     . 

2  medium    

7.8 

Cauliflower          .     .     . 

11.6 

19.1 

Celery  soup,  canned 

2  servings          ...... 

6.6 

Cheese,  American  pale 

1^  cubic  inches                      .     •  • 

0.8 

American  red  .     .     . 

1|  cubic  inches  

0.8 

Cheddar      .... 

1^  cubic  inches  

0.8 

Cottaee  . 

4  cubic  inches  (^  cupful)    .     . 

3.2 

Neufchatel.     ... 
Roquefort  .     .     .     . 

l£  cubic  inches  (j  cupful)    .     . 
1^  cubic  inches  ...... 

1.1 
1.0 

Swiss      

1^  cubic  inches       .          .     .    «- 

0.8 

Chicken  broilers 

1  large  serving 

3.3 

Chocolate  .     .         .     . 

1  generous  half  souare 

0.6 

Cocoa 

2i  tablespoonfuls 

1  0 

Cod  salt    

3.4 

Corn  green 

1  side-dish 

3.6 

Corn  meal      .... 

1.0 

Crackers,  graham    . 

3  crackers    

0.9 

soda       

3  crackers         

0.9 

water                        . 

3  crackers              .               . 

0.9 

Cranberries,  cooked 

7.5 

Cream  

x  cupful  . 

1.8 

Cucumbers     .... 

2  laree 

20.3 

Dates  dried 

4  medium                    .... 

1.0 

Doughnuts                    . 

^  doughnut 

0.8 

APPENDIX 


289 


VI.   Heat  Value  of  Foods  — Continued 


FOOD  (edible  portion) 

• 

APPROXIMATE  MEASURE  op 
IOO-GREAT-CALORY 
PORTION 

WEIGHT  IN 
OUNCES  OF 
IOO-GREAT- 
CALORY 
PORTION 

Eggs   uncooked      

I^T  medium  or  2  small    . 

2.4 

Farina 

1  0 

Figs,  dried     
Flour  rye           

1  large  
j  cupful     

1.1 
1.0 

wheat   entire 

-i  cupful 

1  0 

wheat,  graham    
wheat,  average  high,  medium 

^  cupful     
£  cupful     

1.0 

1.0 

Gelatin               .     . 

4  tablespoonfuls 

1  0 

Grapes 

1  large  bunch 

3  7 

Haddock  

4.9 

Halibut  steaks        . 

1  average  serving 

29 

Ham  fresh  lean 

1  5 

fresh,  medium     

1  average  serving    . 

1.1 

smoked  lean 

1.3 

Herring  whole 

25 

Hominy,  uncooked      .... 

i  cupful     

1.0 

Lamb,  chops,  broiled       .     .     . 
leg  roast 

1  small  chop  .... 
1  average  serving 

1.0 

1  8 

Lard,  refined      
Lemons    .... 

1  tablespoonful  (scant) 
3  medium  

0.4 
8.0 

Lettuce 

50  large  leaves 

20.4 

Liver,  veal,  uncooked 
Macaroni,  uncooked  . 
Macaroons    ....          .     . 

2  small  servings  . 
£  cupful  (4  sticks)  . 

2 

2.9 
1.0 
0.8 

Mackerel,  uncooked   .... 
salt  . 

1  large  serving    .     .     . 

2.5 
1.2 

Marmalade,  orange    .... 
Milk,  condensed,  sweetened 
skimmed    

1  tablespoonful  . 
l~rV  cupful8       .... 
1^  cupfuls   

1.0 
1.1 
9.6 

whole    
Molasses  cane  . 

f  cupful  (half  glass)     . 
I  cupful 

5.1 

1.2 

^  large  serving    . 

8.9 

Mutton,  leg  

1  average  serving    . 

1.8 

Oatmeal,  uncooked     .... 

i  cupful     

0.9 

Olives  green 

7  to  10                      .     . 

1.2 

Onions  fresh 

2  medium 

7.3 

Oranges    

1  very  large   .... 

6.9 

290  HOUSEHOLD   PHYSICS 

VI.    Heat  Value  of  Foods — Continued 


FOOD  (edible  portion) 

APPROXIMATE  MEASURE  OP 
IOO-GREAT-CALORY 
PORTION 

WEIGHT  IN 
OUNCES  OF 
IOO-GREAT- 
CALORY 
PORTION 

Oysters,  canned  .... 

5  oysters  

49 

Parsnips     

1  large 

54 

Pea  soup,  canned     . 
Peaches,  canned      .     .     . 
fresh 

1  large  serving  
1  large  
4  medium 

3.5 
7.5 
S  ^ 

Peanuts     

10  to  12  (double  kernels) 

06 

Peas,  dried,  uncooked  .     . 
canned 

2  tablespoonfuls      .... 
2  servings 

1.6 
6  3 

green      
Pies,  apple      

1  generous  serving 
\  piece  . 

3.5 
1  3 

custard  • 

?  piece  . 

20 

lemon     

-3-  piece  . 

1  4 

mince     

A  piece  . 

1  2 

squash    

•J-  piece  . 

20 

Pineapples,  fresh 

5  slices 

82 

canned    

1  small  serving 

2  3 

Pork,  chops,  medium 
fat,  salt  

1  very  small  serving    .     .     . 

1.1 
05 

Potatoes,  white,  uncooked 
sweet,  uncooked  . 

1  medium      
\  medium      .... 

4.2 
2.9 

Prunes,  dried      .... 

3  large 

1  2 

Raisins  
Rhubarb,  uncooked      .     . 
Rice,  uncooked  .... 
Salmon,  whole    .... 

\  cupful  (packed  solid)    .     . 
3|  cupfuls  (scant)     .... 
2  tablespoonfuls     .... 
1  small  serving  . 

1.0 
15.3 
1.0 

1  7 

Shad,  wrhole   
Shredded  wheat  .... 

1  average  serving   .... 
1  biscuit   

2.2 
1.0 

Spinach,  fresh     .... 
Succotash,  canned  .     .     . 
Sugar    

3  ordinary  servings  (cooked) 
1  average  serving    .     . 
3     lumps      5     tea  spoonfuls 

14.7 
3.6 

Tomatoes,  fresh  .... 
canned   

granulated,  6^  teaspoon- 
fuls  powdered 
4  average  servings  .... 
1-2-  cupfuls  .... 

0.9 
15.5 
156 

Turkev 

1  serving  . 

1  2 

Turnips 

2  large  servings  (2  turnips) 

90 

Veal,  cutlet 

2.3 

APPENDIX 


291 


VI.    Heat  Value  of  Foods  —  Continued 


FOOD  (edible  portion) 

APPROXIMATE  MEASURE  OF 
IOO-GREAT-CALORY 
PORTION 

WEIGHT  IN 
OUNCES  OF 
IOO-GREAT- 
CALORY 
PORTION 

fore  Quarter 

]  thick  slice    

2.3 

hind  Quarter 

23 

Vegetable  soup  canned 

259 

\Valnuts   California 

0.5 

Wheat,  cracked  
Whitefish        

4  nuts  

1.0 
2.4 

Zwiebach 

0.8 

VII.    Tables  of  Measurements 
English  Lineal  Measure 
12  inches  =  1  foot 
3  feet       =  1  yard 
5|  yards    =  1  rod 
320  rods      =  1  mile 

Lineal  Chain  Measure 
7.92  inches  =  1  link 
100  links     =  1  chain 
80  chains  =  1  mile 

Rope  and  Cable  Measure 
6  feet          =  1  fathom 
120  fathoms  =  1  cable's  length 

Cloth  Measure 
2.25  inches  =  1  nail 

4  nails          =  1  quarter 

5  quarters    =  1  ell 


Metric  Lineal 
10  millimeters  = 
10  centimeters  = 
10  decimeters  = 
10  meters 
10  dekameters  = 
10  hektameters  = 
10  kilometers  = 


Measure 
1  centimeter 
1  decimeter 
1  meter 
1  dekameter 
1  hektameter 
1  kilometer 
1  myriameter 


292  HOUSEHOLD   PHYSICS 

Equivalent  values  in  English  and  Metric  Lineal  Measure 

1  inch  =  2.54  centimeters 

1  foot  =  30.48  centimeters 

1  yard  =  91.44  centimeters 

1  rod  =  502.92  centimeters 

1  mile  =  160,934.72  centimeters 

1  centimeter  =  .394  inch 

English  Surface  Measure 

144  square  inches  =  1  square  foot 
9  square  feet      =  1  square  yard 
30|  square  yards  =  1  square  rod 
160  square  rods    =  1  acre 
640  acres  =  1  square  mile 

Architect's  Measure 
1  square  =  100  square  feet 

Metric  Surface  Measure 

100  square  millimeters   =  1  square  centimeter 
100  square  centimeters  =  1  square  decimeter 
100  square  decimeters    =  1  square  meter 
100  square  meters          =  1  square  dekameter 
100  square  dekameters  =  1  square  hektameter 
100  square  hektameters  =  1  square  kilometer 
100  square  kilometers    =  1  square  myriameter 

Equivalent  values  in  English  and  Metric  Measure 

1  square  inch  =  6.45  square  centimeters 

1  square  foot  =  929.03  square  centimeters 

1  square  yard  =  8361.29  square  centimeters 

1  square  rod  =  252,929.04  square  centimeters 

1  square  centimeter  =  .155  square  inch 

English  Measure  Volume 

1728  cubic  inches         =  1  cubic  foot 
27  cubic  feet  =  1  cubic  yard 

A  standard  gallon  contains  231  cubic  inches,  and  a  standard  struck 
bushel  contains  2150.42  cubic  inches. 


APPENDIX  293 

English  Liquid  Measure 

4  gills       =  1  pint 
2  pints      =  1  quart 
4  quarts   =  1  gallon 

English  Dry  Measure 

2  pints     =  1  quart 
4  quarts  =  1  gallon 
2  gallons  =  1  peck 
4  pecks     =  1  bushel 

English  Fluid  Measure 

8  drams    =  1  ounce 
16  ounces  =  1  pint 
2  pints      =  1  quart 
4  quarts  =  1  gallon 

Metric  Measure  of  Volume 

1000  cubic  millimeters  =  1  cubic  centimeter 

1000  cubic  centimeters  =  1  cubic  decimeter 

1000  cubic  decimeters  =  1  cubic  meter 

1000  cubic  meters  =  1  cubic  dekameter 

1000  cubic  dekameters  =  1  cubic  hektameter 

1000  cubic  hektameters  =  1  cubic  kilometer 

1000  cubic  kilometers  =  1  cubic  myriameter 

Metric  Liquid  and  Dry  Measure 

10  milliliters  =  1  centiliter 

10  centiliters  =  1  deciliter 

10  deciliters  =  1  liter 

10  liters  =  1  dekaliter 

10  dekaliters  =  1  hektaliter 

10  hektaliters  =  1  kiloliter 

10  kiloliters  =  1  myrialiter 
The  liter  contains  1  cubic  decimeter  or  1000  cubic  centimeters. 

Equivalent  values  in  English  and  Metric  Volume  Measure 

1  cubic  centimeter  =  .061  cubic  inch 

1  cubic  meter          =  1.308  cubic  yards 

1  liter  =  .908  dry  quart  =  1.057  liquid  quarts 


294 


HOUSEHOLD  PHYSICS 


English  Measures  of  Weight 

16  ounces  =  1  pound 
2000  pounds  =  1  ton 

Metric  Measures  of  Weight 

10  milligrams  =  1  centigram 

10  centigrams  =  1  decigram 

10  decigrams  =  1  gram 

10  grams  =  1  dekagram 

10  dekagrams  =  1  hektogram 

10  hektograms  =  1  kilogram 

10  kilograms  =  1  myriagram 

Equivalent  values  in  English  and  Metric  Measures  of  Weight 

453.6  grams  =  1  pound 
VIII.   Vibrations  of  Musical  Sounds 


Letter C 

Frequency 256 

Interval  between  con- 
secutive tones      .     . 
Interval  between  each 
tone  and  C  .  1 


D 

288 


E 

320 

10       i  < 

9^ 


F 

3411 


G 

384 


A 


I 


B 

480 


IX.    Candle-Power  of  a  Few  Sources  of  Light 

Carbon  Lamp about  f  c.  p.  per  watt 

Tungsten  Lamp    ......     about  ^  c.  p.  per  watt 

Nitrogen  Lamp about  1  c.  p.  per  watt 

Mercury  Vapor  Lamp    ....     about  1  c.  p.  per  watt 
Arc  Light about  1  c.  p.  per  watt 

X.   Terms  and  Abbreviations  in  Electricity 


512 


THING  TO  BE  MEASURED 

UNIT 

LETTER 

Pressure 

Volt 

E 

Current 

Ampere 

I 

Ohm 

R 

Watt 

W 

Electrical  Energy      

Kilowatt 
Watt-hour 
Kilowatt-hour 

Kw 

W-hr. 
Kw-hr. 

APPENDIX 


295 


XI.    Table  of  Densities  and  Specific  Gravities  of  Some  Substances 


SUBSTANCE 

DENSITY 

SPECIFIC 
GRAVITY 

Lbs.  Per 
Cu.   Ft. 

Gms.  Per  c.  c. 

Ash  (dry)     

43.7 

52.8 
66.4 
50.0 
165.6 
53.2 
35.0 
15.0 
550.6 
555.0 
527.5 
1218.8 
75.2 
480.0 
449.0 
709.6 
46.0 
850.0 
64.5 
76.3 
53.1 
28.8 
1348.8 
64.4 
656.3 
31.2 
590.0 
115.1 
455.8 
41.6 
62.5 
431.3 

.70 
.84 
1.062 
.80 
2.65 
.69  to  .852 
.561 
.24 
8.81 
8.88 
8.38  to  8.44 
19.50 
1.22 
7.68 
7.20 
11.36 
.75 
13.6 
1.032 
1.22 
.85 
.46 
21.5 
1.03 
10.5 
.5 
7.84 
1.84 
7.29 
.67 
1.00 
6.9 

.70 
.84 
1.062 
.80 
2.65 
.69  to  .852 
.561 
.24 
8.81 
8.88 
8.38  to  8.44 
19.50 
1.22 
7.68 
7.20 
11.36 
.75 
13.6 
1.032 
1.22 
.85 
.46 
21.5 
1.03 
10.5 
.5 
7.84 
1.84 
7.29 
.67 
1.00 
6.9 

Ash  (green)       
Acetic  Acid       
Alcohol    
Aluminum   
Beech      
Cedar      
Cork  

Copper  (cast)  
Copper  (sheet)      
Brass  

Gold  
Hydrochloric  Acid     .... 
Iron  (wrought)      
Iron  (cast)  

Lead  
Maple 

Mercurv      

Milk  
Nitric  Acid 

Oak 

Pine 

Platinum     .... 

Sea  Water   . 

Silver      .     . 

Spruce 

Steel  
Sulphuric  Acid      .     .          . 

Tin  (cast)    . 

Walnut 

Water 

Zinc 

INDEX 


Numbers  refer  to  pages. 


Absolute  zero 38 

Absorbers 58 

Acceleration  ...  .  252,  255 
Additive  method  in  color  .  .  137 
Air  necessary  for  a  person  .  .  56 

Air  pressure .     264 

Air  pressure,  other  applications 

of 271 

Alcohol  used  in  thermometers  .  4 
Alternating  current  rectified  .  222 

Ammeter 186 

Ammonia  used  in  ice  plant    .     21,  22 

Amperes 174 

Amplitude      .     .     .      70,  71,  79,  258 

Angle  of  incidence 96 

Angle  of  reflection  .....       96 

Annunciator 170 

Anode 213 

Arc  lamp,  automatic    .     .       171,  179 

candle  power  of 130 

Archimedes'  principle       .     .     .     277 

applications  of 278 

Area 227 

Armature  of  generator     .     .     .     159 

Artificial  ice 8 

plant 21,  22 

rinks 22,  23 

Astigmatism 121 

Atmosphere  as  a  refracting  sub- 
stance     107 

Atmospheric  pressure       .     .     .     8,  9 

Atom 212 

Attraction,  law  of  magnetic  .  .  147 
Axis  .  .  .  .  • 100 

Balance  wheel  of  a  watch    .     .  33 

Barometer      ....   265,  266,  267 

Batteries 217 

Beats 78 

Bell,  door  .     . 165 

Binoculars,  field 110 

Blue  132 


Boiling  point .     .     .     .  3,  4,  5,  7,  8,  9 

Boyle's  law 272 

British  Thermal  Unit  (B.  T.  U.), 

definition  of 10 

Brushes  of  generator  ....  159 

Buzzer 165 

Calory,  definition 10 

Calory,  great,  definition  of    .     .  10 

Camera  lens 117 

Camera,  life-sized  picture  .  .  122 
Camera,  pinhole  .  .  .  116,  117 
Candle  power  ....  127,  128 

Candle  power,  measurement  of  129 

Capillarity 275 

Carbon  lamp,  candle  power  of  130 

color  of 136 

Cathode 213 

Center  of  curvature  of  mirror   .  98 

Centigrade  thermometer       .     .  4 

construction  of 4 

Centrifugal  force 256 

Charles'  law        39 

applications  of 39 

applied  to  baking     ...      39,  40 

applied  to  clay  modeling  .     .  40 

other  applications    ....  40 

Chemical  energy 221 

Choroid  coat  of  eye      .     .     .     .  119 

Chromatic  scale 87 

Circuit  breaker 169 

City  system  wiring  diagram      .  200 

Closed  pipes,  resonance  in    .     .  83 

Clothes      . 46 

Clouds 25 

Coal,  as  a  fuel 60,  61 

Cochlea 77 

Coefficient  of  cubical  expansion  35 

linear  expansion 29 

linear  expansion,  table  of  .     .  30 

volume  expansion    ....  35 

Cohesion 11,  16,  259 


297 


298 


INDEX 

Numbers  refer  to  pages. 


Cold  body,  differs  from  hot  body         2 

definition  of 3 

Color 132 

niters 143 

harmony  of     . 140 

how  we  see 137 

nomenclature 140 

of  opaque  objects     ....     134 
of   transparent   and   translu- 
cent objects 135 

screens 141 

Colored  objects,  application  of     135 

Colors,  cause  of 132 

elementary 136 

Commutator  of  generator     .     .     160 

Concave  mirror 98,  100 

Condensation      .     .     .     .    70,  71,  84 

Condenser 203 

Conduction 41,  58 

Conductor,  electrical    .     .       153,  155 

Conductors 41 

Convection 41,  47,  58 

Convection  currents  48,  50,  51,  52,  53 
Convex  mirror    .     .     .     .  •    100,  101 

Cornea  of  the  eye 119 

Counter-electromotive  force      .     193 

Crest 69 

Critical  angle 107 

Crystalline  lens 120 

Current  of  electricity  ....     153 

Dark  lantern 124 

Daylight  lamp 136 

Decorations,    selection    of,    ac- 
cording to  color 136 

Degree,  unit  used  on  thermom- 
eter      5 

Density 278,  279,  280 

Dew 25 

Diamond Ill 

Diffused  light      ......  125 

Discord 86 

Disks,  colored 138 

Dispersion 132 

Distillation 19 

fractional 20 

Domestic  science,  relation  of,  to 

physics        2 

Dominant 86 

Double  boiler  18 


Drafts  in  chimney 48 

Dress  goods,   selection  of,   ac- 
cording to  colors      ....  136 

Driven  pulley 241 

Driver  pulley 241 

Dry  cell 219 

Dyes .134 

Dynamics 248 


Ear        

drum      .     .     .     . 

external      .     .     . 

how  we  hear   . 

inner      .     .     .     . 

middle  .  .  .  . 
Edison  storage  cell 
Efficiency  .  .  .  . 
Electric  clock 


77 

77 

77 

77 

77 

77 

223 

235 

169 


curling  iron 181 

door  latch  172 

flat  iron 180 

gas  lighter 172 

grill 182 

mangle 183 

percolator  181 

soldering  iron 181 

stove 181 

toaster 181 

Electrical  current 154 

application  of  heating  effect  of  176 

chemical  relation  of  ...  212 

D  C  pulsating,  made  steady  162 

heating  effect  of 173 

induced 202 

magnetic  effect  of  .  .  .  .  163 

magnetic  field  about  a  163 

motion  producing  effect  of  .  184 

through  a  helix 164 

Electrical  energy 174 

generator,  simple  .  .  .  .  155 

generator,  simple  AC.  .  .  156 

generator,  simple  DC.  .  .  160 

power 174 

Electrical  pressure  ....  200 

alternating  current  .  .  .  .  159 

amount  of 154 

curve  of,  in  A  C  generator  .  157 

curve  of,  in  D  C  generator  .  161 

direct  current 159 

direction  of  ....  154 


INDEX 

Numbers  refer  to  pages. 


299 


generation  of        153 

nature  of 154 

of  a  voltaic  cell 215 

stepped  up 204 

Electrical  units 173 

Electricity 153 

analogous  to  water        .       154,  155 

relation  to  magnetism  .     .     .  153 

static 224 

Electrodes 217 

Electrolyte 213 

Electrolytic  cell 212 

chemical  action  in    .     .     .     .  212 

copper  sulphate 213 

parts  of 213 

sulphuric  acid 214 

Electro-magnet  .     .     .     .       164,  165 

applications  of 165 

in  a  coil  of  wire 201 

other  applications  of     ...  172 

poles  of 164,  165 

Electro-plating 215 

Electro-typing 215 

Energy 91 

definition  of 1 

kinetic 257 

of  motion 256 

English    system    compared    to 

metric 229,  230 

of  measurement 227 

Ether 57 

vibrations  in 3 

waves  in 91 

Eustachian  tube 77 

Evaporization 23 

Expansion 29 

effect  on  balance  wheel  of  a 

watch 33 

effect  on  glass  ware       ...  34 

effect  on  pendulum  of  a  clock  32 

effect  on  water  pipes     ...  37 

of  gases 38 

other  effects  of 34 

peculiar   effects   on   water     35,  36 

tank 52 

Eye       119,  137 

defective 120 


Fahrenheit  thermometer 
Fifth  .     .     .     .     , 


4,  5 

87 


Fireless  cooker 43 

First  class  lever 234 

Flowing  of   gases   and  liquids     260 

Fluorescence      91 

Focal  length        99,  112 

Focus 100,  111 

principal 99 

Fog        25 

Foods,  heating  value  ...      63,  64 
Foot-pound    ......       231,  232 

Force 230,  233 

arm 233 

centrifugal 256 

moment 233 

parallelogram  of 250 

to  overcome  friction      .     .     .     256 
to  overcome  inertia       .     .     .     255 

units  of 231 

Forced  systems  of  ventilation     55,  56 

Fourth 87 

Freezing,  effect  on  water  pipes       37 

point 1,  4,  5,  8,  9 

point,  definition  of  ....         6 

points,  table  of 7 

Frequency      .     .      70,  71,  73,  79,  86 

Friction 256 

Fuels 68 

Fundamental 80 

Fusion,  heat  of,  definition  of     .       11 

Galvanometer 185 

Gas,  artificial 60 

Gases 259 

Gases  and  liquids  through  pipes  260 

Gas  meter 62 

Gas,  natural 60 

Gelatin,  extraction  of  ....  9 

Gram-centimeter 231 

Gravitation 257 

Newton's  three  laws  of      .     .  257 

Gravity  cell    .......  220 

Green 132 

Hail 25 

Half-step 87 

Half-tone  picture  printing     .     .  140 

Harmony 85 

laws  of 86 

of  color 14° 


300 


INDEX 

Numbers  refer  to  pages. 


Heat,  absorption  of     ....  2 

and  heat  measurement      .     .  1 

capacity 26 

changed   from    one   form    to 

another  2 

definition  of 2 

insensible 57 

kinds  of 2 

molecular 2 

nature  of 1 

necessary  for  one  person   .     .  64 

of  fusion 11 

of  fusion,  effect  on  climate     14,  15 
of  fusion,  protection  by     .     .  14 
of  vaporization    ....      15,  16 
of  vaporization,  effect  on  cli- 
mate    21 

of  vaporization,  other  effects 

of        21 

quantity  of 10 


radiant  .... 

sensible       .     .     . 

sources  of  ... 

transference  of     . 

travels   .... 

units       .... 

units  compared    . 

value  of  foods 

value  of  fuels  .     . 
Helmholtz  resonators 
Horse-power       .     . 
Hot  air  heating  .     . 


.     .         2 
.     .      57 

.  .  60 
.  .  41 
.  .  2 
.  ;  10 
.  .10 
.  63,  64 
60,  61,  62 
.  80,  81 
.  .  245 
50 


Hot  bodies,  definition  of  ...         3 
Hot  body,  how  different  from  a 

cold  body 2 

Hot  water  bottle 28 

Hot  water  heating  system     51 ,  52,  53 

Hot  water  tank 50,  51 

House  circuit,  wiring  diagram  of     209 
Hydraulic  elevator       .     .     .     .  '  261 

Hygrometer 24 

Hypermetropia 120 


Ice  cream  freezer  .  . 
Ice  cream,  making  of  . 
Iceless  refrigerators  . 
Ices,  freezer  of  ... 
Ices,  making  of  ... 
Illumination  . 


13 

6 

22 

13 

6 

127 


problems  of     ......     130 


Image 97,  112 

how  to  find  in  a  plane  mirror  97 

in  a  concave  mirror       ...  99 

in  a  convex  mirror   .     .     .     .  100 

real 98 

through    a    converging    lens  112, 

113,  114,  115 

through  a  diverging  lens  .     .  11.6 

virtual 98 

Incandescent  lamp,  carbon  .     .  176 

gas  filled 178 

mercury  vapor 178 

tungsten 177 

Incidence,  angle  of      ....  105 

Incident  ray 96,  104 

Inclined  plane    .     233,  239,  240,  241 

height  of 240 

length  of     .......  240 

Index  of  refraction,  absolute     .  106 

relative 106 

Indigo  .........  132 

Induction 200 

coil    .     .     .,    .     .     .     ./  .     .  203 

coil,  uses  of 204 

mutual 202 

self    .     .    ..     .  ,..     ....  202 

Inertia 202,  249,  255 

Insensible  heat 2 

Insulation 44 

Insulators       .......  41 

Insulators,  electrical    ....  155 

Intensity  of  illumination  .     .     .  127 

Intensity  of  sound 79 

Interference .  78 

Interval,  musical     .......  87 

Ion 212 

lonization 212 

Iris  of  the  eye 119 

Isobars 269 

Isotherms  269 


Kilowatt-hours 174 

Kilowatts 174 

Kinetic  energy 257 

Kitchen  range 49 

Lantern  slide 123 

Lead  of  a  screw 244 

Length 227 


INDEX 

Numbers  refer  to  pages. 


301 


Lens,  achromatic 133 

condensing 123 

converging Ill 

diverging Ill 

Lenses Ill 

Lever    .     .     .  233,  234,  235,  236,  237 

classes  of 234 

Light 01 

velocity  of  .     .     .     .     .92,  93,  94 

Lighthouse  reflector    ....  109 

Light,  nature  of 91 

theory  of  production  of     .     .  91 

waves,  propagation  of  92 

Line  drop 207 

Lines  of  force 148,  163 

properties  of 149 

Liquids 259 

Lodestone 146 

Long-sightedness 120 

Loudness 79 

Luminous  bodies 91 

Machines       .......  233 

Magnet,  electro 164 

field  of 147 

permanent 152 

poles  of 146 

tempo  rary 152 

Magnetic   fields,    characteristic  152 

needle 163 

poles  of  the  earth     ....  147 

substances 150 

Magnetism 146 

of  earth 147 

theory  of 149 

Magnetized  piece  of  iron  com- 
pared to  one  not  magnetized  150 

Magnetizing  iron 151 

Magnifying  glass 124 

Major  scale 86 

triad 86 

Mass 227,  255 

Matter,  composition  of     ...  2 

definition  of 1 

Mechanical  advantage     .     .     .  234 

Mechanics  of  fluids     ....  259 

of  solids 227 

Melting  point 1 

Mercury  in  contact  with  glass  275 

in  thermometers                       .  4,  8 


vapor  lamp,  candle  power  of  130 

vapor  lamp,  color  of     ...  136 

Meters  for  A  C 190 

Metric  system  of  measurement  229 
Miller,    Dr.    Dayton,    of    Case 

School  of  Applied  Science  81 

Mirror 96 

concave 98 

convex  . 100 

parabolical 98 

peculiarly  shaped     .     .     .     .  102 

spherical 98 

Mist 25 

Mixing  colored  lights        .     .     .  137 
Molecular  construction  of  mat- 
ter        2 

heat 2 

Molecules 7,  11 

Moment 233 

Moments,  law  of 234 

Momentum    . 254 

Motion       .     .     .      230,  231,  248,  252 

energy  of 250 

formulae    for    uniformly    ac- 
celerated        253 

Newton's  three  laws  of     248,  249 

picture  machine 123 

Motor  and  generator  compared  191 

Motor,  compound 194 

DC 190 

series 194 

shunt     ......       194,  195 

small 197 

use  of,  in  home 199 

Music,  basis  for 85 

Musical  instruments   ....  89 

interval 87 

Myopia 120 

Natural   system  of  ventilation  55 

Negative  plate 119 

Newton's  three  laws  of  gravita- 
tion      257 

motion 248,  249 

Nitrogen  lamp,  candle-power  of  130 

Noise 85 

Non-conducting  materials     .     41,  42 

magnetic  substances     .     .     .  150 

Octave 87 

Ohm          174 


302 


INDEX 

Numbers  refer  to  pages. 


Ohm's  law 175 

Opaque  objects  .     .     .     .58,  94,  133 

Open  pipes,  resonance  in      .     .  84 

Optical  center 112 

Orange 132 

Overtones 80 

Paints 135 

Parabolical  mirror 98 

Parallelogram  of  forces    .     .     .  250 

Pascal's  law 261 

Pencil  of  rays 96,  97 

Pendulum 258 

laws  of        258 

of  a  clock,  compensating  .     .  32 

Penumbra 95 

Period 70,  71 

natural  free 76 

Phosphorescence 91 

Photograph,  how  made     .     .  118,  119 

Photometer 129 

Physics,  definition  of  ....  1 
relation      of,      to      domestic 

science 2 

Pigments        135 

colored        138 

mixing  colored 138 

Pitch 79 

international  standard       .     .  89 

of  screw 244 

standard 88 

Pivot 233 

Plane  mirror 97,  100 

Plaster 45 

lath 45 

Polarization 218 

Power 245 

delivered  by  pulleys      .     .     .  246 

Pressure,  application  of  water  262 

applied        7 

effect  of,  on  boiling  point     .  8,  9 

effect  of,  on  freezing  point     .  8 
how  to  calculate,  in  an  open 

vessel 262 

kettle .  9 

water 260 

Primary  cells 220 

coil 202 

Principal  axis 112 

of  mirror 98 


Principal  focus 99,  112 

Prismatic  window  glass   .     .     .     109 

Prisms,  refracting 109 

Projecting  lantern 122 

Pulley  ....     233,  241,  242,  243 

Pump,  force   . 270 

lift 269 

Quality  of  Sound     .     .     .     .     79,  80 

Radiant  heat 2,  91 

Radiation 41,  57 

Radiators 58 

Radical 212 

Rain      .........       25 

Range,  kitchen 49 

Rarefaction 70,  71,  84 

Red 132 

Reflected  ray 97 

Reflection      ....     96,  103,  104 

Reflection,  law  of 96 

total       .     ....     ...     108 

Reflectors 58 

Refracted  ray 104 

Refraction 103 

angle  of 105 

index  of 105 

law  of 104 

Refrigerator 44 

tested 13 

uses  of 12 

Repulsion,  law  of,  magnetic      .     147 

Resistance 155 

what  determines  amount  of  .     155 

Resonance 76 

in  closed  pipes 83 

in  open  pipes 84 

principle  of 76,  78 

Resonators 80,  81 

Retina,  eye 120,  137 

Roemer's    method    of    finding 

velocity  of  light    ....       92 

Salt  on  ice,  effect  of    ...      13,  14 

Saturation  point 23 

Scale,  chromatic 87 

major 86 

tempered 88 

Sclerotic  coat  of  eye    .     .     .     .     119 
Screw 233,  244 


INDEX 

Numbers  refer  to  pages. 


303 


Second  class  lever 234 

Secondary  cell 221 

Secondary  coil 202 

See,  how  we 120 

Sensible  heat 2 

Shades 138 

Shadows 94,  95 

Sheathing 45 

Short-sightedness 120 

Siphon 271 

Slip-rings 159 

Snow 25 

Solids 259 

Sound 74 

characteristics  of      ....       79 
effect  of  temperature  on  ve- 
locity of 76 

intensity  of 79 

interference  of 78 

nature  of 74 

quality  of 79 

reinforcement  of  ...  78,  83 
things  necessary  for  ...  74 

velocity  of 75,  84 

waves,  analysis  of  .  .  .  80,  81 
waves,  how  they  travel  .  .  75 
waves,  photographs  of  .  82,  83 

Space 227 

Specific  gravity  278,  279,  280,  281,  282 
method  of  calculating  .     .  281,  282 

Specific  heat 27 

effect  on  climate       ....       28 

Spectrum,  solar 132 

Speed 252 

Spherical  mirror 98 

Standard  candle 129 

pitch 88 

Starting  box 192 

need  of        193 

Static  electricity 224 

Steam  cooker 18 

heating 16,  17,  18 

Storage  cell 220 

charging  of 222 

dry,  lead 222 

Edison        223 

lead,  wet 221 

uses  of 222 

Studding 45 

Sub  dominant 86 


Subtractive  method     ....  138 

Sugar,  manufacture  of     ...  9 

Surface  tension .     .     .   ' .     .     .  273 

applications  of    273,  274,  275,  276 

Telegraph  relay 167 

sounder 166 

system 167 

Telephone      .    . 210 

switch  hoard,  automatic   .     .  172 
Temperature  at  which  water  is 

densest 36 

and  quantity  of  heat  compared  10 

definition  of 3 

Tempered  scale 88 

Thermometer,   alcohol  used  in  4 

centigrade 4 

changing  from  centigrade 
reading  to  Fahrenheit  read- 
ing    5,  6 

expansion  involved  in  ...  4 

Fahrenheit 4 

fixed  points  of 4,  5 

kinds  of 4 

mercury  in 4 

relation    of    centigrade    and 

Fahrenheit  scales       ...  5 

uses  of 4 

Thermos  bottle 44,  58 

Thermostat 30,  31 

Third  class  lever 234 

Third,  major 87 

Three  color  printing  process      .  142 

Three  phase  system    ....  208 

Three  primary  colors  ....  136 

Three  states  of  matter     .     .     .  259 

Time 227 

Tints 138 

Tonic 86 

Transformer  .     .  ^204,  205,  206,  207 

advantages  and  uses  of      .  206,  207 

Translucent  object      ....  133 

Transparent  object      ....  133 

Triad,  major 86 

Trough 69 

Tungsten  lamp,  candle-power  of  130 

Umbra 95 

Unison 87 

Units  of  measurement     .     .     .  227 

velocity 252 


304 


INDEX 

Numbers  refer,  to  pages. 


Vacuum 44 

pan 9 

Vapor  tension 7 

Velocity     ........  252 

Ventilation 54,  55,  56 

Vernier 267 

Vibrating  strings,  laws  of     .     .  81 

Vibration,  complete     ....  70 

Violet 132 

Volt 174 

Voltaic  cell 217 

addwater. 219 

closed  circuit 220 

Daniell 220 

dry 219 

gravity        220 

open  circuit 218 

secondary  or  storage     .     .     .  220 

sulphuric  acid 217 

wet  salammoniac      ....  218 

Voltmeter 187 

Volume 227 

expansion         35 

Walls  of  houses 45 

Water  in  contact  with  glass       .  274 
Water  vapor  in  the  air  23,  24,  25,  26 

Water,  when  densest  ....  36 


Watt 174 

Watt-hour 174 

Watt-hour  meter 191 

Wattmeter 188 

Wave,  characteristics  of  longi- 
tudinal          70,  71 

transverse        69,  70 

Wave  length       .     .      70,  71,  73,  132 
longitudinal     .     .     .  69,  71,  72,  75 
motion        .......       67 

motion,  examples  of      ...       67 

origin  of 68 

transverse        .     .        69,  70,  71,  92 

velocity  of 72,  73 

Weather-board 45 

Weather  maps 268 

Wedge .233,244 

Weighing  balance   .     .     .       235,  236 

Weight 233 

Weight-arm 233 

moment 233 

Wheel  and  axle       .     .   233,  238,  239 
Work    .     .     .     f     .     .   '.     .  173, 231 

Work-in     .    ... 235 

Work-out  .     .     .    :..    .     .     .     .     235 

Work,  units  of 231 

Yellow  .  132 


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